Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C23×Dic278 |
| Sylow | C139 ⋊ C23×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D139 |
| commutator | C2×C139 | C25 |
| Frattini | C2 | C24×D139 |
| Fitting | C23×C4×C139 | C2 |
| socle | C24×C139 | C22 |
| hypercenter | C23×C4 | D139 |
| hypocenter | C139 | C23×Q8 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C24 ◁ C23×C4 | |
850 conjugacy classes of subgroups.
2248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804674, #31806327, #31806338, … |
| maximal normal subgroup of | #31804674, #31806327, #31806338, … |
| maximal quotient of | C23×Dic139⋊C4, C23×C4⋊Dic139, C22×C4×Dic278, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 1373);