Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #13676 |
394 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 394 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 111 |
| transitive degree | μt(G) = 2528 |
A minimal faithful permutation representation — 3 generators on 111 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)(81,87)(82,90)(84,93)(85,95)(86,98)(88,101)(89,103)(91,105)(92,107)(94,97)(96,102)(99,104)(100,111)(106,108)(109,110);(80,82,85,92)(81,86,89,100)(83,90,95,107)(84,91,97,108)(87,98,103,111)(88,99,96,109)(93,105,94,106)(101,104,102,110);(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)(80,81,85,89)(82,86,92,100)(83,87,95,103)(84,96,97,88)(90,104,107,110)(91,99,108,109)(93,101,94,102)(98,106,111,105)Polycyclic presentation:
2^8,79|a^2=h,b^2=h,f^2=h,b^a=bd,c^a=ce,f^a=fg,i^a=i^78,e^b=efgh,g^b=gh,d^c=df,f^c=fh,g^c=gh,e^d=egh,f^d=fh,f^e=fh1156 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 90294);