Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C22 |
| direct product | Q8×C139⋊C8 |
| Sylow | C139 ⋊ C8×Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D139 |
| commutator | C2×C139 | C22×C8 |
| Fitting | C4×Q8×C139 | C2 |
| socle | C22×C139 | C22×C4 |
| hypercenter | C4×Q8 | D139 |
| hypocenter | C139 | C8×Q8 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2×C4 ◁ C4×Q8 | |
102 conjugacy classes of subgroups.
1420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31805201, SD16×C139⋊C8, #31805208, … |
| maximal normal subgroup of | #31805201, SD16×C139⋊C8, #31805208, … |
| maximal quotient of | C4⋊C4×C139⋊C8, #31806963, #31807123, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 675);