Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1595 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#1617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C23×C23 |
| prime radical | C23×C23 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C22×C4×C23 ◁ G | |
202 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 68 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)(24,25,30,45)(26,35,37,52)(27,40,46,42)(28,33,29,34)(31,47,48,36)(32,44,55,43)(38,51,39,53)(41,49,54,50);(24,26,28,38)(25,31,33,49)(27,41,43,36)(29,39,30,37)(32,51,40,35)(34,50,45,48)(42,52,55,53)(44,47,46,54);(24,25,29,34)(26,31,39,50)(27,42,44,32)(28,33,30,45)(35,36,53,54)(37,48,38,49)(40,43,55,46)(41,52,47,51)529 conjugacy classes — view the full character table.
| maximal subgroup of | C23×#12221, C23×#12222, C23×#12223, … |
| maximal normal subgroup of | C23×#12221, C23×#12222, C23×#12223, … |
| maximal quotient of | C23×#7792, C23×#7794, C23×#7806, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 349);