Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3003 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C26 |
| direct product | C23×#3004 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C24×C23 |
| prime radical | C23×#525 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C23×C4×C23 ◁ G | |
738 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 224 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) = 736 |
A minimal faithful permutation representation — 4 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)(24,25)(26,27)(28,29)(30,36)(31,39)(32,34)(33,37)(35,41)(38,43)(40,42);(28,30,32,38)(29,33,34,42)(31,40,41,37)(35,43,39,36);(25,27);(29,34)(33,42)(35,39)(36,43)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#9519, C23×#18136, C23×#18146, … |
| maximal normal subgroup of | C23×#9519, C23×#18136, C23×#18146, … |
| maximal quotient of | C23×#18133, C23×#18138, C23×#18143, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1736);