Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2075 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C24×C23 | D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
256 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(28,29)(30,33)(31,32)(34,35)(36,37,38,41,39,42,43,40);(24,25)(26,27)(29,32)(33,35);(25,27)(28,30,31,34)(29,33,32,35)(37,40)(38,43)(41,42)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#7079, C23×#7087, C23×#12278, … |
| maximal normal subgroup of | C23×#7079, C23×#7087, C23×#12278, … |
| maximal quotient of | C23×#10615, C23×#10617, C23×#10621, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 807);