Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42 |
| direct product | #376×D71 |
| Fitting | #376×C71 ⋊ C2 |
| Sylow | C71 ⋊ C2×#376 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C2×C71 | C22×C42 |
| Frattini | C23 | C23×D71 |
| Fitting | #376×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | #376 | D71 |
| hypocenter | C71 | C2×#376 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ #376 | |
840 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1274×D71, #31886852, #1300×D71, … |
| maximal normal subgroup of | #1274×D71, #31886852, #1300×D71, … |
| maximal quotient of | C4×#95×D71, C4×#17985844, #376×Dic71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 6835);