Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C27 |
| direct product | C2×#10597399 |
| Fitting | C25×C19 ⋊ C2 |
| Sylow | C19 ⋊ C2×#120 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D19 |
| commutator, cosocle | C22×C19 | C24 |
| Frattini | C22 | C23×D19 |
| Fitting | C25×C19 | C2 |
| socle | C23×C19 | C23 |
| hypercenter | C25 | D19 |
| hypocenter | C19 | C2×#120 |
| LCS | G ▷ C22×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ C25 | |
662 conjugacy classes of subgroups.
| transitive degree | μt(G) = 304 |
316 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #14564040, #14564086, #14564088, … |
| maximal normal subgroup of | #14564040, #14564086, #14564088, … |
| maximal quotient of | C2×#11926400, C2×#11926417, C2×#11926423, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1035);