Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | Q8×#11765865 |
| Fitting | C2×C4×Q8×C71 ⋊ C2 |
| Sylow | C71 ⋊ Q8×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C25 |
| Frattini | C22 | C24×D71 |
| Fitting | C2×C4×Q8×C71 | C2 |
| hypercenter | C2×C4×Q8 | D71 |
| hypocenter | C71 | Q8×#41 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×Q8 | |
1068 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31889493, #31889497, #31964326, … |
| maximal normal subgroup of | #31889493, #31889497, #31964326, … |
| maximal quotient of | C4⋊C4×#11765865, Q8×#14556085, Q8×#14556087, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 18091);