Finite Group DatabasebetaFinite Group Databasebeta| order | 8912 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C22 |
| unambiguous semidirect product | C22⋊#14555805 |
| unambiguous semidirect product | (C2×#14555805)⋊C2 |
| Fitting | C22×C557 ⋊ C4 |
| Sylow | C557 ⋊ C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×#14555805 |
| commutator, socle | C2×C557 | C2×C4 |
| Fitting | C22×C557 | C4 |
| hypercenter | C22 | #14555805 |
| hypocenter | C557 | C22⋊C4 |
| LCS | G ▷ C2×C557 ▷ C557 | |
| UCS | C1 ◁ C2 ◁ C22 | |
34 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,557|a^2=d,b^a=bc,e^a=e^118,e^d=e^556566 conjugacy classes — view the full character table.
| maximal subgroup of | #31821555, #31821556, C2×C22⋊#14555805, … |
| maximal normal subgroup of | #31821555, #31821556, C2×C22⋊#14555805, … |
| maximal quotient of | (C2×#14555805)⋊C4, C22⋊#17984962, #31821554, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8912, 45);