Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×#1425 ⋊ C2 |
| Sylow | C53 ⋊ #13701 |
180 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 181 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)(54,57)(55,64)(56,72)(58,79)(59,88)(60,81)(61,80)(62,82)(63,93)(65,98)(66,105)(67,99)(68,78)(69,100)(70,108)(71,115)(73,119)(74,126)(75,121)(76,120)(77,122)(83,139)(84,134)(85,143)(86,135)(87,136)(89,144)(90,132)(91,138)(92,145)(94,150)(95,148)(96,130)(97,149)(101,156)(102,157)(103,131)(104,155)(106,158)(107,137)(109,159)(110,162)(111,160)(112,118)(113,161)(114,165)(116,154)(117,167)(123,170)(124,147)(125,171)(127,174)(128,169)(129,173)(133,141)(140,176)(142,175)(146,177)(151,179)(152,178)(153,168)(163,180)(164,172)(166,181);(54,56,71,114,60,75,85,124,59,74,116,152,89,127,87,92,62,77,101,146,91,129,86,125,61,76,117,166,84,123,58,73)(55,63,83,111,67,95,102,110,66,94,140,163,106,151,104,113,69,97,142,164,107,153,103,112,68,96,141,128,90,109,65,70)(57,72,115,165,81,121,143,147,88,126,154,178,144,174,136,145,82,122,156,177,138,173,135,171,80,120,167,181,134,170,79,119)(64,93,139,160,99,148,157,162,105,150,176,180,158,179,155,161,100,149,175,172,137,168,131,118,78,130,133,169,132,159,98,108);(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)(54,55,62,69)(56,70,77,113)(57,78,82,105)(58,83,87,142)(59,68,61,66)(60,90,91,106)(63,92,97,73)(64,88,100,80)(65,101,104,71)(67,89,107,84)(72,118,122,162)(74,112,76,110)(75,128,129,163)(79,133,136,176)(81,137,138,99)(85,141,86,140)(93,147,149,171)(94,124,96,125)(95,152,153,166)(98,154,155,167)(102,116,103,117)(108,126,161,120)(109,146,151,114)(111,127,164,123)(115,131,156,157)(119,130,145,150)(121,172,173,160)(132,144,158,134)(135,139,143,175)(148,165,168,177)(159,178,179,181)(169,174,180,170)Polycyclic presentation:
2^8,53|a^2=h,b^2=df,d^2=fg,e^2=h,f^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eh,f^a=fg,g^a=gh,i^a=i^52,e^c=eh,i^c=i^521034 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90439);