Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16 · Schur multiplier (H2) = C26 |
| direct product | C23×C71⋊C16 |
| derived, Sylow | C71 ⋊ C23×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C8 | D71 |
| commutator, hypocenter | C71 | C23×C16 |
| Frattini | C8 | C23×D71 |
| Fitting | C23×C8×C71 | C2 |
| socle | C24×C71 | C8 |
| LCS | G ▷ C71 | |
| UCS | C1 ◁ C23×C8 | |
440 conjugacy classes of subgroups.
2368 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22586417, C2×#22586418, #31912295, … |
| maximal normal subgroup of | C2×#22586417, C2×#22586418, #31912295, … |
| maximal quotient of | C22×C4×C71⋊C16, C22×C22⋊(C71⋊C16), C22×C4⋊(C71⋊C16), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 17603);