Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C2 |
| direct product | C23×#1671 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C23 | #121 |
| commutator, Frattini, cosocle | C42 | C23×C23 |
| prime radical | C2×D4×C23 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
166 conjugacy classes of subgroups; only the 72 normal subgroups are shown.
This group has 166 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) = 39 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,28)(26,30)(29,31)(32,33,35,38)(34,36,39,37);(24,25,26,28,27,29,30,31);(33,36)(34,39)(37,38)667 conjugacy classes — view the full character table.
| maximal subgroup of | C2×C23×#1671, C23×#19105, C23×#19124, … |
| maximal normal subgroup of | C2×C23×#1671, C23×#19105, C23×#19124, … |
| maximal quotient of | C23×#8642, C23×#9215, C23×#9217, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 403);