Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C2×C23×#135 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G | |
220 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 68 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)(28,29,34,38)(30,39,42,57)(31,36,33,48)(32,44,47,58)(35,50,53,41)(37,43,55,46)(40,56,49,54)(45,51,59,52);(28,30)(29,35)(31,40)(32,45)(33,49)(34,42)(36,51)(37,54)(38,53)(39,44)(41,46)(43,50)(47,59)(48,52)(55,56)(57,58);(25,27)(28,31,34,33)(29,36,38,48)(30,40,42,49)(32,43,47,46)(35,51,53,52)(37,44,55,58)(39,56,57,54)(41,45,50,59)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2189, C23×#33516, C23×#33519, … |
| maximal normal subgroup of | C2×C23×#2189, C23×#33516, C23×#33519, … |
| maximal quotient of | C23×#12107, C23×#12163, C23×#12283, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 921);