Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2127 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2135 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | C2×#99 |
| commutator | C2×C4 | C22×C4×C23 |
| Frattini, cosocle | C2×Q8 | C23×C23 |
| prime radical | C2×#41×C23 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×#41×C23 ◁ G | |
230 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 84 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)(24,25,29,34,30,35,27,32)(26,36,39,54,40,51,37,53)(28,42,41,52,44,33,45,50)(31,46,47,43,48,55,49,38);(24,26,30,40)(25,31,35,48)(27,39,29,37)(28,43,44,38)(32,49,34,47)(33,51,42,36)(41,46,45,55)(50,53,52,54);(24,27,30,29)(25,32,35,34)(26,37,40,39)(28,41,44,45)(31,47,48,49)(33,50,42,52)(36,53,51,54)(38,46,43,55)529 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12712, C23×#12713, C23×#12721, … |
| maximal normal subgroup of | C23×#12712, C23×#12713, C23×#12721, … |
| maximal quotient of | C23×#11434, C23×#11450, C23×#11481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 867);