Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D19 |
| Fitting | C19×H(5,𝔽2) ⋊ C2 |
| Sylow | C19 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D19 |
| commutator, socle, cosocle | C2×C19 | C25 |
| Fitting | C19×H(5,𝔽2) | C2 |
| hypercenter | H(5,𝔽2) | D19 |
| hypocenter | C19 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C19 ▷ C19 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
| transitive degree | μt(G) = 152 |
187 conjugacy classes — view the full character table.
| maximal subgroup of | D19×#453, D19×#455, #14572989, … |
| maximal normal subgroup of | D19×#453, D19×#455, #14572989, … |
| maximal quotient of | D19×#518, D19×#520, #14576839, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 1378);