Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2180 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#2180 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #442 |
| commutator | C8 | C22×C4×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×#135 | C22 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C23×#97 ◁ G | |
142 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 72 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 55 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)(26,36,38,47)(27,40)(28,32)(29,44)(30,35)(31,37,48,54)(33,41)(34,46)(39,51,45,53)(42,52,55,49)(43,50);(24,26)(25,31)(27,37)(28,42)(29,45)(30,38)(32,47)(33,51)(34,52)(35,48)(36,50)(39,46)(40,53)(41,54)(43,55)(44,49);(24,27,29,28,30,41,46,43)(25,32,34,40,35,50,44,33)(26,37,45,42,38,54,39,55)(31,47,52,53,48,36,49,51)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2180, C23×#33468, C23×#33469, … |
| maximal normal subgroup of | C2×C23×#2180, C23×#33468, C23×#33469, … |
| maximal quotient of | C23×#12065, C23×#12066, C23×#12077, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 912);