Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#14555768 |
| Fitting | C4×C8×C139 ⋊ C2 |
| Sylow | C139 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D139 |
| commutator | C2×C139 | C2×C42 |
| Frattini | C2×C4 | C22×D139 |
| Fitting | C4×C8×C139 | C2 |
| socle | C22×C139 | C22×C4 |
| hypercenter | C4×C8 | D139 |
| hypocenter | C139 | C4×M16 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
142 conjugacy classes of subgroups.
2248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14555768, #31804683, #31804690, … |
| maximal normal subgroup of | C8×#14555768, #31804683, #31804690, … |
| maximal quotient of | C8×#14555768, #31804690, #31804698, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 499);