Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C26 |
| direct product | C2×C23×#451 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C24×C23 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C23 ◁ C23×C4×C23 ◁ G | |
740 conjugacy classes of subgroups; only the 248 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4)(5,6)(7,8,11,14)(9,15,17,22)(10,18,20,13)(12,19,21,16);(7,9,11,17)(8,12,14,21)(10,19,20,16)(13,22,18,15);(4,6)874 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9040, C23×#9258, C23×#9924, … |
| maximal normal subgroup of | C23×#9040, C23×#9258, C23×#9924, … |
| maximal quotient of | C2×C23×#1602, C2×C23×#1614, C2×C23×#1605, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1731);