Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1664 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| prime radical | C2×D4×C23 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
184 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 184 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) = 55 |
| transitive degree | μt(G) = 1472 |
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)(24,25,29,33)(26,34,36,39)(27,32,28,31)(30,37,38,35)(40,41,45,43)(42,48,51,55)(44,52,54,47)(46,53,49,50);(24,26)(25,30)(27,37)(28,35)(29,36)(31,39)(32,34)(33,38)(40,42,45,51)(41,46,43,49)(44,53,54,50)(47,55,52,48);(24,26)(25,30)(27,35)(28,37)(29,36)(31,34)(32,39)(33,38)(40,43,45,41)(42,49,51,46)(44,47,54,52)(48,53,55,50)460 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1664, C23×#18987, C23×#18990, … |
| maximal normal subgroup of | C2×C23×#1664, C23×#18987, C23×#18990, … |
| maximal quotient of | C23×#7764, C23×#7765, C23×#7766, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 396);