Finite Group DatabasebetaFinite Group Databasebeta| order | 2944 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C23 · Schur multiplier (H2) = C26 |
| direct product | C2×C4×D8×C23 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C23 | D4 |
| commutator | C4 | C23×C4×C23 |
| Frattini, cosocle | C2×C4 | C24×C23 |
| socle | C23×C23 | C2×D4 |
| prime radical | C22×D8×C23 | C2 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C23 ◁ C2×C42×C23 ◁ G | |
616 conjugacy classes of subgroups.
| minimal degree | μ(G) = 37 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 generators on 37 points:
(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37);(3,4,5,6);(7,8,9,10,11,12,13,14);(8,14)(9,13)(10,12)1288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C23×#8947, C23×#8951, C23×#9657, … |
| maximal normal subgroup of | C23×#8947, C23×#8951, C23×#9657, … |
| maximal quotient of | C2×C8×D8×C23, C2×C23×#1581, C2×C23×#1589, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2944, 1668);