Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C4×C8×C127 ⋊ C2 |
| Sylow | C127 ⋊ #405 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8 | C2×D127 |
| commutator | C2×C127 | C2×C42 |
| Frattini | C2×C4 | C22×D127 |
| Fitting | C4×C8×C127 | C2 |
| socle | C22×C127 | C22×C4 |
| hypercenter | C4×C8 | D127 |
| hypocenter | C127 | #405 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C2×C8 ◁ C4×C8 | |
130 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,127|a^2=d,b^2=e,d^2=f,c^b=cf,g^c=g^1262056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30640325, #30640328, #30640487, … |
| maximal normal subgroup of | #30640325, #30640328, #30640487, … |
| maximal quotient of | C8×#14523231, #30637012, #30637018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 503);