Finite Group DatabasebetaFinite Group Databasebeta| order | 12608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #137×C197 ⋊ C2 |
| Sylow | C197 ⋊ #578 |
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 229 |
| transitive degree | μt(G) = 6304 |
A minimal faithful permutation representation — 4 generators on 229 points:
(1,2)(3,4)(5,6)(7,8)(9,10)(11,12)(13,14)(15,16)(17,18)(19,20)(21,22)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34)(35,36)(37,38)(39,40)(41,42)(43,44)(45,46)(47,48)(49,50)(51,52)(53,54)(55,56)(57,58)(59,60)(61,62)(63,64)(65,66)(67,68)(69,70)(71,72)(73,74)(75,76)(77,78)(79,80)(81,82)(83,84)(85,86)(87,88)(89,90)(91,92)(93,94)(95,96)(97,98)(99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(201,212)(205,219)(209,223)(213,225)(217,228)(220,226)(222,229)(224,227);(198,201)(199,205)(200,209)(202,213)(203,212)(204,217)(206,220)(207,219)(208,222)(210,224)(211,223)(214,226)(215,227)(216,225)(218,228)(221,229);(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(54,55)(56,57)(58,59)(60,61)(62,63)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(84,85)(86,87)(88,89)(90,91)(92,93)(94,95)(96,97)(98,99)(100,101)(102,103)(104,105)(106,107)(108,109)(110,111)(112,113)(114,115)(116,117)(118,119)(120,121)(122,123)(124,125)(126,127)(128,129)(130,131)(132,133)(134,135)(136,137)(138,139)(140,141)(142,143)(144,145)(146,147)(148,149)(150,151)(152,153)(154,155)(156,157)(158,159)(160,161)(162,163)(164,165)(166,167)(168,169)(170,171)(172,173)(174,175)(176,177)(178,179)(180,181)(182,183)(184,185)(186,187)(188,189)(190,191)(192,193)(194,195)(196,197)(198,200,203,211)(199,204,207,218)(201,209,212,223)(202,215,216,210)(205,217,219,228)(206,221,214,208)(213,227,225,224)(220,229,226,222);(198,199,203,207)(200,208,211,221)(201,205,212,219)(202,214,216,206)(204,215,218,210)(209,222,223,229)(213,226,225,220)(217,227,228,224)Polycyclic presentation:
2^6,197|a^2=f,b^2=f,e^2=f,b^a=be,e^a=ef,e^b=ef,g^b=g^196,d^c=df,g^d=g^1961100 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #38754482, #38754484, #38754486, … |
| maximal normal subgroup of | #38754482, #38754484, #38754486, … |
| maximal quotient of | #38751243, #38751244, #38751311, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(12608, 1365);