Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2987 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C23 | C24 |
| commutator | C22 | C23×C4×C23 |
| Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C22×C23 | C23×C4 |
| prime radical | C23×C23 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C23 ◁ G | |
314 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 248 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) = 1472 |
A minimal faithful permutation representation — 4 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)(26,32)(27,30)(28,31)(29,34)(33,38)(35,37)(36,39)(40,41,43,47,44,46,50,53)(42,45,49,52,48,51,54,55);(24,26,28,34)(25,29,31,32)(27,35,36,33)(30,38,39,37)(40,42)(41,45)(43,49)(44,48)(46,51)(47,52)(50,54)(53,55);(24,27,28,36)(25,30,31,39)(26,33,34,35)(29,37,32,38)(41,46)(42,48)(47,53)(49,54);(25,31)(29,32)(30,39)(37,38)(42,48)(45,51)(49,54)(52,55)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#8919, C23×#9006, C23×#9008, … |
| maximal normal subgroup of | C23×#8919, C23×#9006, C23×#9008, … |
| maximal quotient of | C23×#20539, C23×#20542, C23×#20576, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1719);