Finite Group DatabasebetaFinite Group Databasebeta| order | 20224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C79 ⋊ #11540 |
262 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 79 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)(80,82,85,96,86,93,83,94)(81,88,87,101,91,105,89,92)(84,99,100,103,98,95,97,110)(90,107,102,109,108,104,106,111);(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)(81,87,91,89)(82,93)(84,98)(88,92,105,101)(90,102,108,106)(94,96)(97,100)(104,109,107,111);(80,81,84,90,85,89,100,106,86,91,98,108,83,87,97,102)(82,92,95,109,96,105,110,107,93,101,99,111,94,88,103,104)Polycyclic presentation:
2^8,79|a^2=e,b^2=f,c^2=fg,d^2=h,e^2=g,g^2=h,b^a=bd,c^a=cg,d^a=df,f^a=fh,c^b=ch,e^b=efh,i^b=i^78,e^c=eh,e^d=eh1282 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(20224, 79078);