Finite Group DatabasebetaFinite Group Databasebeta| order | 8128 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic254 |
| Sylow | C127 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D127 |
| commutator | C2×C127 | C25 |
| Frattini | C2 | C24×D127 |
| Fitting | C23×C4×C127 | C2 |
| socle | C24×C127 | C22 |
| hypercenter | C23×C4 | D127 |
| hypocenter | C127 | C23×Q8 |
| LCS | G ▷ C2×C127 ▷ C127 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
2056 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30637000, #30638653, #30638664, … |
| maximal normal subgroup of | #30637000, #30638653, #30638664, … |
| maximal quotient of | C23×Dic127⋊C4, C23×C4⋊Dic127, C22×C4×Dic254, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8128, 1373);