Finite Group DatabasebetaFinite Group Databasebeta| order | 20096 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | #508×C157 ⋊ C2 |
| Sylow | C157 ⋊ #2262 |
106 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 106 conjugacy classes of subgroups — too many to draw. Only its 41 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 221 |
| transitive degree | μt(G) = 10048 |
A minimal faithful permutation representation — 3 generators on 221 points:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,124,126,128,130,132,134,136,138,140,142,144,146,148,150,152,154,156,157,155,153,151,149,147,145,143,141,139,137,135,133,131,129,127,125,123,121,119,117,115,113,111,109,107,105,103,101,99,97,95,93,91,89,87,85,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(158,161,164,179)(159,166,170,169)(160,172,176,175)(162,177,183,210)(163,178,186,211)(165,187,189,197)(167,190,194,193)(168,191,196,184)(171,198,199,206)(173,200,203,202)(174,201,205,185)(180,207,213,212)(181,208,215,214)(182,209,216,219)(188,195,217,221)(192,204,218,220);(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)(158,160)(159,165)(161,172)(162,181)(163,185)(164,176)(166,187)(167,192)(168,195)(169,197)(170,189)(171,180)(173,182)(174,178)(175,179)(177,208)(183,215)(184,188)(186,201)(190,204)(191,217)(193,220)(194,218)(196,221)(198,207)(199,213)(200,209)(202,219)(203,216)(205,211)(206,212)(210,214);(158,159)(160,171)(161,166)(162,180)(163,184)(164,170)(165,173)(167,182)(168,178)(169,179)(172,198)(174,204)(175,206)(176,199)(177,207)(181,195)(183,213)(185,192)(186,191)(187,200)(188,214)(189,203)(190,209)(193,219)(194,216)(196,211)(197,202)(201,218)(205,220)(208,217)(210,212)(215,221)Polycyclic presentation:
2^7,157|c^2=g,d^2=ef,e^2=fg,f^2=g,b^a=bd,d^a=de,e^a=ef,f^a=fg,d^b=de,e^b=ef,f^b=fg,h^b=h^1561754 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20096, 6817);