Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2199 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#2201 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C2×D4 | C23×C23 |
| prime radical | C23×H(5,𝔽2) | C22 |
| LCS | G ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C22×C23 ◁ C2×D4×C23 ◁ G | |
226 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 56 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)(26,34)(27,31)(28,32)(29,33)(30,36)(35,51)(37,50)(38,49)(39,45)(40,46)(41,48)(42,52)(43,53)(44,54)(47,55);(24,26,29,37)(25,30,33,43)(27,38,40,35)(28,36,41,53)(31,44,46,42)(32,34,48,50)(39,54,55,52)(45,49,47,51);(24,27,29,40)(25,31,33,46)(26,35,37,38)(28,39,41,55)(30,42,43,44)(32,47,48,45)(34,49,50,51)(36,52,53,54)391 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#13679, C23×#13680, C2×C23×#2201, … |
| maximal normal subgroup of | C23×#13679, C23×#13680, C2×C23×#2201, … |
| maximal quotient of | C23×#12095, C23×#12101, C23×#12125, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 933);