Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C79×#1422 ⋊ C2 |
| Sylow | C79 ⋊ #13647 |
186 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 186 conjugacy classes of subgroups — too many to draw. Only its 81 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)(80,83,85,102,86,95,107,126,84,101,104,132,105,113,135,139,87,103,108,134,109,118,137,141,106,133,117,140,136,88,111,112)(81,89,91,82,92,97,121,98,93,115,122,99,124,128,142,130,94,116,123,100,125,129,143,131,90,114,119,96,120,110,138,127);(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)(81,88)(83,92)(84,99)(85,97)(86,98)(87,100)(89,111)(90,118)(91,112)(93,95)(94,113)(96,106)(101,124)(102,121)(103,125)(104,128)(105,130)(107,115)(108,129)(109,131)(110,117)(114,137)(116,135)(119,141)(120,133)(122,126)(123,139)(127,136)(132,142)(134,143)(138,140);(80,81,85,91,86,92,107,121,84,93,104,122,105,124,135,142,87,94,108,123,109,125,137,143,106,90,117,119,136,120,111,138)(82,95,97,126,98,101,115,132,99,113,128,139,130,103,116,134,100,118,129,141,131,133,114,140,96,88,110,112,127,83,89,102)Polycyclic presentation:
2^8,79|a^2=e,c^2=e,d^2=h,e^2=f,f^2=g,g^2=h,b^a=bd,d^a=dh,d^b=dh,i^b=i^78,i^c=i^782296 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90131);