Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2984 |
| 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 | |
364 conjugacy classes of subgroups; only the 272 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 272 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 47 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,28,29,27,31,26,30)(32,33)(34,40)(35,38)(36,39)(37,42)(41,46)(43,45)(44,47);(24,26,27,28)(25,29,31,30)(32,34,36,42)(33,37,39,40)(35,43,44,41)(38,46,47,45);(24,26,27,28)(25,30,31,29)(32,35,36,44)(33,38,39,47)(34,41,42,43)(37,45,40,46);(25,31)(29,30)(33,39)(37,40)(38,47)(45,46)1150 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#9164, C23×#9166, C23×#9244, … |
| maximal normal subgroup of | C23×#9164, C23×#9166, C23×#9244, … |
| maximal quotient of | C23×#20535, C23×#20572, C23×#20573, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1716);