Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×C139⋊C8 |
| derived, Sylow | C139 ⋊ C2×C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D139 |
| commutator, hypocenter | C139 | C2×C4×C8 |
| Frattini | C2×C4 | C22×D139 |
| Fitting | C2×C42×C139 | C2 |
| socle | C23×C139 | C2×C4 |
| LCS | G ▷ C139 | |
| UCS | C1 ◁ C2×C42 | |
162 conjugacy classes of subgroups.
2272 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139⋊#1273, #31804238, #31804240, … |
| maximal normal subgroup of | C139⋊#1273, #31804238, #31804240, … |
| maximal quotient of | C2×C8×C139⋊C8, C2×#22580674, M16×C139⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 495);