Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C79×#1497 ⋊ C2 |
| Sylow | C79 ⋊ #8501 |
616 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 103 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:
(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(80,83)(81,88)(82,93)(84,99)(85,97)(86,98)(87,100)(89,105)(90,103)(91,104)(92,106)(94,110)(95,109)(96,108)(101,111)(102,107)(112,115,117,128)(113,119,120,133)(114,123,125,140)(116,129,130,127)(118,131,122,136)(121,135,134,126)(124,141,142,139)(132,138,137,143);(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)(83,93)(84,96)(85,94)(86,95)(88,100)(89,102)(90,92)(91,101)(97,110)(98,109)(99,108)(103,106)(104,111)(105,107)(112,114)(113,118)(115,123)(116,124)(117,125)(119,131)(120,122)(121,132)(126,143)(127,139)(128,140)(129,141)(130,142)(133,136)(134,137)(135,138);(80,81,85,90,86,91,84,89)(82,92,96,87,95,102,94,101)(83,88,97,103,98,104,99,105)(93,107,108,111,109,106,110,100)(112,113)(114,122,125,118)(115,126,128,135)(116,121)(117,120)(119,127,133,129)(123,138)(124,137,142,132)(130,134)(131,139)(136,141)(140,143)Polycyclic presentation:
2^8,79|a^2=f,c^2=g,d^2=h,e^2=g,f^2=h,b^a=bd,c^a=ce,d^a=dg,d^b=dh,e^b=eh,f^b=fgh,i^b=i^78,d^c=dh,e^c=eg,f^c=fg1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 61979);