Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | C8×Dic254 |
| Sylow | C127 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D127 |
| commutator | C2×C127 | C22×C8 |
| Frattini | C2×C4 | C22×D127 |
| Fitting | C4×C8×C127 | C2 |
| socle | C22×C127 | C22×C4 |
| hypercenter | C4×C8 | D127 |
| hypocenter | C127 | C8×Q8 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
102 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636708, #30636710, C8×#14523236, … |
| maximal normal subgroup of | #30636708, #30636710, C8×#14523236, … |
| maximal quotient of | C8×C4⋊Dic127, C8×Dic127⋊C4, #30639286, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 674);