Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D139 |
| Fitting | C22×Q8×C139 ⋊ C2 |
| Sylow | C139 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D139 |
| commutator | C2×C139 | C25 |
| Frattini | C2 | C24×D139 |
| Fitting | C22×Q8×C139 | C2 |
| socle | C23×C139 | C23 |
| hypercenter | C22×Q8 | D139 |
| hypocenter | C139 | C23×Q8 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
850 conjugacy classes of subgroups.
1420 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31806326, #31806337, #391×D139, … |
| maximal normal subgroup of | #31806326, #31806337, #391×D139, … |
| maximal quotient of | C22×C4⋊C4×D139, C2×C4×Q8×D139, C22×#17984807, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1372);