Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#2210 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C2×C23×D16 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C4×C8×C23 ◁ G | |
170 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 64 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)(25,27)(28,29)(30,33)(31,34)(32,40)(35,39)(36,38)(37,41)(42,43);(24,25,26,27)(29,33)(34,41)(35,42)(36,40);(29,34)(31,39)(32,38)(33,41)(35,36)(37,43)(40,42)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2210, C23×#33579, C23×#33580, … |
| maximal normal subgroup of | C2×C23×#2210, C23×#33579, C23×#33580, … |
| maximal quotient of | C23×#12418, C23×#12422, C23×#12428, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 942);