Finite Group DatabasebetaFinite Group Databasebeta| order | 8992 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×C22⋊D281 |
| Fitting | C22×C4×C281 ⋊ C2 |
| Sylow | C281 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D281 |
| commutator | C2×C281 | C22×C4 |
| Frattini | C22 | C22×D281 |
| Fitting | C22×C4×C281 | C2 |
| socle | C22×C281 | C23 |
| hypercenter | C22×C4 | D281 |
| hypocenter | C281 | C4×D4 |
| LCS | G ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C2×C4 ◁ C22×C4 | |
94 conjugacy classes of subgroups.
2260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31823526, C8×C22⋊D281, #31823531, … |
| maximal normal subgroup of | #31823526, C8×C22⋊D281, #31823531, … |
| maximal quotient of | C4×C22⋊Dic281, C4×#17985115, C4×#17985117, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8992, 107);