Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊(C127⋊C8) |
| Sylow | C127 ⋊ C2×C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C2×D127 |
| commutator | C2×C127 | C22×C8 |
| Frattini | C2×C4 | C22×D127 |
| Fitting | C2×C42×C127 | C2 |
| socle | C23×C127 | C2×C4 |
| hypercenter | C2×C42 | D127 |
| hypocenter | C127 | C2×C4⋊C8 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C22×C4 ◁ C2×C42 | |
138 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30636564, #30636565, #30636570, … |
| maximal normal subgroup of | #30636564, #30636565, #30636570, … |
| maximal quotient of | C2×#22549627, C2×#22549629, #30637478, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 570);