Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #2184 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#2229 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ C4×C8×C23 ◁ G | |
124 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 2944 |
A minimal faithful permutation representation — 3 generators on 63 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,27,29)(26,30,31,28)(32,33,35,38)(34,42,43,60)(36,48,46,61)(37,51,47,41)(39,55,53,44)(40,57,54,50)(45,62,52,58)(49,59,63,56);(24,26,27,31)(25,28,29,30)(33,38)(39,53)(40,54)(41,51)(42,60)(48,61)(56,59)(58,62);(32,34,35,43)(33,39,38,53)(36,49,46,63)(37,52,47,45)(40,58,54,62)(41,59,51,56)(42,61,60,48)(44,57,55,50)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2229, C23×#33626, C23×#33628, … |
| maximal normal subgroup of | C2×C23×#2229, C23×#33626, C23×#33628, … |
| maximal quotient of | C23×#12814, C23×#12936, C23×#12938, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 961);