Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#1814 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #121 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C2×C23 | #380 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C22×C4×C23 ◁ G | |
256 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 116 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)(26,35)(27,40,42,47)(28,43)(29,33)(30,34)(31,37)(32,41,48,44)(36,45,52,55)(38,46)(39,50)(49,51,54,53);(24,26,28,37,30,39,29,38)(25,31,33,35,34,46,43,50)(27,36,41,51,42,52,44,53)(32,45,47,49,48,55,40,54);(24,27)(25,32)(26,36)(28,41)(29,44)(30,42)(31,45)(33,47)(34,48)(35,49)(37,51)(38,53)(39,52)(40,43)(46,55)(50,54)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12747, C23×#12750, C23×#12751, … |
| maximal normal subgroup of | C23×#12747, C23×#12750, C23×#12751, … |
| maximal quotient of | C23×#8604, C23×#8605, C23×#8606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 546);