Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C23 · Schur multiplier (H2) = C22×C4 |
| direct product | C23×#1757 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C23 | C22⋊C4 |
| commutator | C22 | C2×C42×C23 |
| Frattini, cosocle | C22×C4 | C23×C23 |
| socle | C2×C23 | C4×C22⋊C4 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C23 ◁ C22×C8×C23 ◁ G | |
284 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 284 conjugacy classes of subgroups — too many to draw. Only its 148 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)(24,25,28,32,29,33,40,46)(26,34,37,48,36,30,41,43)(27,31,38,44,39,45,51,54)(35,47,50,55,49,42,52,53);(24,26)(25,30,33,34)(27,35)(28,37)(29,36)(31,42,45,47)(32,43,46,48)(38,50)(39,49)(40,41)(44,53,54,55)(51,52);(24,27,28,38,29,39,40,51)(25,31,32,44,33,45,46,54)(26,35,37,50,36,49,41,52)(30,42,43,53,34,47,48,55)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7207, C23×#7208, C23×#12613, … |
| maximal normal subgroup of | C23×#7207, C23×#7208, C23×#12613, … |
| maximal quotient of | C23×#8156, C23×#8157, C23×#8158, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 489);