Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25 |
| direct product | #95×D19 |
| Fitting | C19×#95 ⋊ C2 |
| Sylow | C19 ⋊ C2×#95 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D19 |
| commutator | C2×C19 | C2×C42 |
| Fitting | C19×#95 | C2 |
| socle, cosocle | C23×C19 | C23 |
| prime radical | C23×D19 | C22 |
| hypercenter | #95 | D19 |
| hypocenter | C19 | C2×#95 |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C23 ◁ #95 | |
330 conjugacy classes of subgroups.
| transitive degree | μt(G) = 608 |
220 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#327, D19×#328, #14562136, … |
| maximal normal subgroup of | D19×#327, D19×#328, #14562136, … |
| maximal quotient of | #95×Dic19, (C2×D19)⋊#95, Dic19⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 392);