Finite Group DatabasebetaFinite Group Databasebeta| order | 1248 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C3×C13 · Schur multiplier (H2) = C22×C4 |
| direct product | C3×C13×#127 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C3×C13 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C3×C13 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C3×C13 ◁ G | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 24 |
| transitive degree | μt(G) = 624 |
A minimal faithful permutation representation — 3 generators on 24 points:
(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(18,20)(22,23);(21,22,24,23);(17,18,19,20)(21,23,24,22)546 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1248, 1141);