Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2008 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#2009 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #392 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C4×C23 ◁ G | |
348 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 88 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 55 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)(26,36)(27,40)(28,34)(29,33)(30,35)(31,38)(32,42)(37,45)(39,50)(41,49)(43,48)(44,46)(47,53)(51,52)(54,55);(24,26)(25,31)(27,37)(28,44)(29,38)(30,39)(32,47)(33,50)(34,36)(35,46)(40,51)(41,54)(42,52)(43,53)(45,49)(48,55);(24,27,30,43)(25,32,35,49)(26,37,39,53)(28,42,29,41)(31,45,46,47)(33,40,34,48)(36,51,50,55)(38,54,44,52)529 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2009, C23×#23412, C23×#23873, … |
| maximal normal subgroup of | C2×C23×#2009, C23×#23412, C23×#23873, … |
| maximal quotient of | C23×#9931, C23×#9933, C23×#9935, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 741);