Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2221 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#2223 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #466 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×#472 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C23×#131 ◁ G | |
144 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 60 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)(25,31)(26,37)(27,40)(28,29)(32,41)(33,48)(34,45)(35,44)(36,46)(38,53)(39,42)(43,49)(50,55)(51,54);(24,25,32,44,29,35,27,31,30,36,40,45,28,34,41,46)(26,33,47,55,37,49,38,43,39,50,52,48,42,51,53,54);(24,26)(25,33)(27,38)(28,42)(29,37)(30,39)(31,43)(32,47)(34,51)(35,49)(36,50)(40,52)(41,53)(44,55)(45,48)(46,54)598 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2223, C23×#33617, C23×#33618, … |
| maximal normal subgroup of | C2×C23×#2223, C23×#33617, C23×#33618, … |
| maximal quotient of | C23×#12432, C23×#12435, C23×#12441, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 955);