Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#362×C79 ⋊ C2 |
| Sylow | C79 ⋊ #13390 |
382 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 143 |
| transitive degree | μt(G) = 5056 |
A minimal faithful permutation representation — 3 generators on 143 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)(80,83,84,100,86,102,106,103)(81,88,89,116,91,117,104,118)(82,93,94,125,97,99,96,131)(85,108,105,114,109,137,119,101)(87,110,92,122,113,115,112,143)(90,120,107,133,121,134,138,98)(95,128,127,126,130,140,129,136)(111,135,123,141,142,124,139,132);(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)(80,82)(81,87)(83,99)(84,96)(85,95)(86,97)(88,115)(89,112)(90,111)(91,113)(92,104)(93,102)(94,106)(98,132)(100,125)(101,136)(103,131)(105,129)(107,139)(108,140)(109,130)(110,117)(114,126)(116,122)(118,143)(119,127)(120,124)(121,142)(123,138)(128,137)(133,141)(134,135);(80,81,86,91)(82,92,97,112)(83,98,102,133)(84,104,106,89)(85,107,109,138)(87,96,113,94)(88,114,117,101)(90,119,121,105)(93,124,99,135)(95,111,130,142)(100,134,103,120)(108,118,137,116)(110,128,115,140)(122,136,143,126)(123,127,139,129)(125,141,131,132)Polycyclic presentation:
2^8,79|a^2=h,c^2=d,d^2=h,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,c^b=cf,d^b=dh,i^b=i^78,e^c=egh,f^c=fh,g^c=gh,i^c=i^781282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 88792);