Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #465 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×C23×#492 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C2×C23×#127 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C2×C42×C23 ◁ G | |
656 conjugacy classes of subgroups; only the 264 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(4,6)(8,11)(9,13)(12,14);(7,8,9,11,10,12,13,14);(3,4,5,6)1012 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9063, C23×#9064, C23×#9732, … |
| maximal normal subgroup of | C23×#9063, C23×#9064, C23×#9732, … |
| maximal quotient of | C2×C23×#1705, C2×C23×#1706, C2×C23×#1707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1875);