Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1636 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
188 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 2944 |
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)(24,25,29,32)(26,33,35,38)(27,31,28,36)(30,37,39,34)(40,41,46,50)(42,51,43,54)(44,49,45,48)(47,53,55,52);(24,26)(25,30)(27,34)(28,37)(29,35)(31,38)(32,39)(33,36)(40,42,46,43)(41,47,50,55)(44,53,45,52)(48,54,49,51);(24,27,29,28)(25,31,32,36)(26,34,35,37)(30,38,39,33)(40,43,46,42)(41,47,50,55)(44,52,45,53)(48,54,49,51)598 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1636, C23×#18494, C23×#18519, … |
| maximal normal subgroup of | C2×C23×#1636, C23×#18494, C23×#18519, … |
| maximal quotient of | C23×#7763, C23×#7769, C23×#7771, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 368);