Finite Group DatabasebetaFinite Group Databasebeta| order | 5312 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D83 |
| Fitting | H(5,𝔽2)×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D83 |
| commutator, socle | C2×C83 | C25 |
| Fitting | H(5,𝔽2)×C83 | C2 |
| hypercenter | H(5,𝔽2) | D83 |
| hypocenter | C83 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C83 ▷ C83 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
731 conjugacy classes — view the full character table.
| maximal subgroup of | #453×D83, #455×D83, #24916817, … |
| maximal normal subgroup of | #453×D83, #455×D83, #24916817, … |
| maximal quotient of | #518×D83, #520×D83, #24920667, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5312, 1378);