Finite Group DatabasebetaFinite Group Databasebeta| order | 9088 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | D4×#11765849 |
| Sylow | C71 ⋊ D4×M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D71 |
| commutator, socle | C22×C71 | C23×C4 |
| Fitting | C2×C4×D4×C71 | C2 |
| hypercenter | C2×C4×D4 | D71 |
| hypocenter | C71 | D4×M16 |
| LCS | G ▷ C22×C71 ▷ C71 | |
| UCS | C1 ◁ C2×C4 ◁ C2×C4×D4 | |
544 conjugacy classes of subgroups.
1450 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31891778, #31891782, #31891792, … |
| maximal normal subgroup of | #31891778, #31891782, #31891792, … |
| maximal quotient of | D8×#11765849, #31968883, SD16×#11765849, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(9088, 13247);