Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C26 · Schur multiplier (H2) = C214 |
| direct product | C22×#41×D71 |
| Fitting | C22×#41×C71 ⋊ C2 |
| Sylow | C71 ⋊ C23×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D71 |
| commutator | C2×C71 | C26 |
| Frattini | C2 | C25×D71 |
| Fitting | C22×#41×C71 | C2 |
| socle | C23×C71 | C24 |
| hypercenter | C22×#41 | D71 |
| hypocenter | C71 | C23×#41 |
| LCS | G ▷ C2×C71 ▷ C71 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
6520 conjugacy classes of subgroups.
1480 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1780×D71, #31996563, #31996567, … |
| maximal normal subgroup of | #1780×D71, #31996563, #31996567, … |
| maximal quotient of | C22×#117×D71, C22×C4×D4×D71, C22×C4×Q8×D71, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 19306);