Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#10597386 |
| Fitting | C22×D4×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D19 |
| commutator, cosocle | C22×C19 | C24 |
| Frattini | C22 | C23×D19 |
| Fitting | C22×D4×C19 | C2 |
| socle | C23×C19 | C23 |
| hypercenter | C22×D4 | D19 |
| hypocenter | C19 | C2×#127 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C22×D4 | |
498 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
208 conjugacy classes — view the full character table.
| maximal subgroup of | #14564030, #14564031, #14564033, … |
| maximal normal subgroup of | #14564030, #14564031, #14564033, … |
| maximal quotient of | C2×#11926413, C2×#11926444, C2×#11926445, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1088);