Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | H(5,𝔽2)×D127 |
| Fitting | H(5,𝔽2)×C127 ⋊ C2 |
| Sylow | C127 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C24×D127 |
| commutator, socle | C2×C127 | C25 |
| Fitting | H(5,𝔽2)×C127 | C2 |
| hypercenter | H(5,𝔽2) | D127 |
| hypocenter | C127 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2 ◁ H(5,𝔽2) | |
898 conjugacy classes of subgroups.
1105 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #453×D127, #455×D127, #30648084, … |
| maximal normal subgroup of | #453×D127, #455×D127, #30648084, … |
| maximal quotient of | #518×D127, #520×D127, #30651934, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1378);