Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2141 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D8 |
| commutator | C8 | C22×C4×C23 |
| Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×C23 | D8 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G | |
220 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 104 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 59 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 59 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)(30,39)(31,36)(32,45)(33,49)(34,38)(35,41)(37,47)(40,53)(42,59)(43,56)(44,54)(46,52)(48,55)(50,57)(51,58);(28,30,34,43)(29,35,38,51)(31,42,33,40)(32,46,48,57)(36,52,49,50)(37,53,54,59)(39,55,56,45)(41,44,58,47);(28,31,34,33)(29,36,38,49)(30,40,43,42)(32,44,48,47)(35,50,51,52)(37,45,54,55)(39,53,56,59)(41,57,58,46)736 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12648, C23×#12742, C23×#12751, … |
| maximal normal subgroup of | C23×#12648, C23×#12742, C23×#12751, … |
| maximal quotient of | C23×#11594, C23×#11650, C23×#11662, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 873);