Finite Group DatabasebetaFinite Group Databasebeta| order | 8992 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#14555886 |
| Sylow | C281 ⋊ C4⋊C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C2×D281 |
| commutator | C2×C281 | C2×C8 |
| Fitting | C42×C281 | C2 |
| socle | C22×C281 | C2×C4 |
| hypercenter | C42 | D281 |
| hypocenter | C281 | C4⋊C8 |
| LCS | G ▷ C2×C281 ▷ C281 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,281|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^2802260 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#14555886, #31823192, Q8⋊#14555886, … |
| maximal normal subgroup of | D4⋊#14555886, #31823192, Q8⋊#14555886, … |
| maximal quotient of | #31823214, #31823216, #31823218, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8992, 76);