Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C23 · Schur multiplier (H2) = C2×C4 |
| direct product | C23×#1391 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C23 | #99 |
| commutator | C23 | C42×C23 |
| Frattini, cosocle | C2×#41 | C22×C23 |
| socle | C2×C23 | #342 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C23 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
166 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 60 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 — 2 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)(26,34)(27,38,39,31)(28,32)(29,33)(30,35,42,48)(36,46)(37,47)(40,51,52,44)(41,45)(43,49,53,55)(50,54);(24,26,28,36,29,37,41,50)(25,30,32,43,33,42,45,53)(27,35,40,49,39,48,52,55)(31,34,44,46,38,47,51,54)598 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7398, C23×#7399, C23×#7406, … |
| maximal normal subgroup of | C23×#7398, C23×#7399, C23×#7406, … |
| maximal quotient of | C23×#7188, C23×#7204, C23×#7214, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 123);