Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C139 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D139 |
| commutator | C22×C139 | C22×C4 |
| Fitting | C25×C139 | C2 |
| socle | C23×C139 | C23 |
| hypercenter | C25 | D139 |
| hypocenter | C139 | #379 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=f,b^a=bd,c^a=ce,g^a=g^1382236 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C139⋊#1304, #31806318, #31806319, … |
| maximal normal subgroup of | C139⋊#1304, #31806318, #31806319, … |
| maximal quotient of | #31804627, #31804645, #31804675, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 405);