Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | C79×#2244 ⋊ C2 |
| Sylow | C79 ⋊ #12465 |
196 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 55 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:
(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)(81,89)(83,97)(84,93)(85,94)(86,96)(87,101)(88,104)(90,107)(91,109)(92,99)(95,98)(100,105)(102,108)(103,106)(110,111);(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)(80,81,88,103,85,90,84,100,86,91,99,110,98,102,83,87)(82,89,104,106,94,107,93,105,96,109,92,111,95,108,97,101);(81,87)(82,92)(83,88)(84,99)(85,98)(90,110)(91,100)(93,94)(95,97)(96,104)(101,106)(102,103)(105,111)(107,108)Polycyclic presentation:
2^8,79|b^2=dg,d^2=fh,e^2=gh,f^2=h,g^2=h,b^a=bd,c^a=ce,d^a=df,e^a=eg,f^a=fh,g^a=gh,e^b=eh,d^c=dh,e^c=eg,g^c=gh,i^c=i^781045 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 83968);