Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D137 |
| Fitting | H(5,𝔽2)×C137 ⋊ C2 |
| Sylow | C137 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D137 |
| commutator, socle | C2×C137 | C25 |
| Fitting | H(5,𝔽2)×C137 | C2 |
| hypercenter | H(5,𝔽2) | D137 |
| hypocenter | C137 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D137, #455×D137, #31790143, … |
| maximal normal subgroup of | #453×D137, #455×D137, #31790143, … |
| maximal quotient of | #518×D137, #520×D137, #31793993, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1378);