Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
| direct product | C2×#16861119 |
| Sylow | C127 ⋊ C2×#97 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D127 |
| commutator | C2×C127 | C2×C42 |
| Frattini | C2×C4 | C22×D127 |
| Fitting | C22×C8×C127 | C2 |
| socle | C23×C127 | C2×C4 |
| hypercenter | C22×C8 | D127 |
| hypocenter | C127 | C2×#97 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22×C4 ◁ C22×C8 | |
146 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636809, #30636813, #97×Dic127, … |
| maximal normal subgroup of | #30636809, #30636813, #97×Dic127, … |
| maximal quotient of | C2×#22549597, C2×#22549598, #30637019, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 497);