Finite Group DatabasebetaFinite Group Databasebeta| order | 8992 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#17985125 |
| Fitting | C2×Q8×C281 ⋊ C2 |
| Sylow | C281 ⋊ C2×SD16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D281 |
| commutator | C4×C281 | C23 |
| Frattini | C4 | C22×D281 |
| Fitting | C2×Q8×C281 | C2 |
| socle | C22×C281 | D4 |
| hypercenter | C2×Q8 | D281 |
| hypocenter | C281 | C2×SD16 |
| LCS | G ▷ C4×C281 ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
68 conjugacy classes of subgroups.
1414 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31823548, C4×#17985125, #31823561, … |
| maximal normal subgroup of | #31823548, C4×#17985125, #31823561, … |
| maximal quotient of | C2×#22582799, C2×#22582803, C2×#22582810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8992, 159);