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×#2237 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | C2×D8 |
| commutator, Frattini, cosocle | C2×C8 | C23×C23 |
| prime radical | C23×C23 | D8 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ C22×C8×C23 ◁ G | |
132 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 60 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) = 1472 |
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)(26,29)(27,28)(30,31)(32,33,37,42)(34,38,45,53)(35,39,48,55)(36,49,47,41)(40,56,54,46)(43,50,59,62)(44,60,58,52)(51,63,61,57);(25,28)(29,31)(32,34,37,45)(33,38,42,53)(35,43,48,59)(36,44,47,58)(39,50,55,62)(40,51,54,61)(41,52,49,60)(46,57,56,63);(24,26,27,30)(25,29,28,31)(33,39)(35,46)(36,47)(38,50)(40,41)(42,55)(43,57)(44,58)(48,56)(49,54)(51,52)(53,62)(59,63)(60,61)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#2237, C23×#33645, C23×#33647, … |
| maximal normal subgroup of | C2×C23×#2237, C23×#33645, C23×#33647, … |
| maximal quotient of | C23×#12868, C23×#12921, C23×#12994, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 969);