Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| isoclinism | isoclinic class of D71 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C64 · Schur multiplier (H2) = C2 |
| direct product | C64×D71 |
| Fitting | C64×C71 ⋊ C2 |
| derived, Sylow | C71 ⋊ C2×C64 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C64 | D71 |
| commutator, hypocenter | C71 | C2×C64 |
| Frattini | C32 | C2×D71 |
| Fitting | C64×C71 | C2 |
| socle | C2×C71 | C2×C32 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C64 | |
40 conjugacy classes of subgroups.
2368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D71, #31885362, C2×C64×D71, … |
| maximal normal subgroup of | C128×D71, #31885362, C2×C64×D71, … |
| maximal quotient of | C64×Dic71, (C2×D71)⋊C64, Dic71⋊C64, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 2718);