Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C139 ⋊ #424 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D139 |
| commutator, socle | C22×C139 | C22×C4 |
| Fitting | C2×M16×C139 | C2 |
| hypercenter | C2×M16 | D139 |
| hypocenter | C139 | #424 |
| LCS | G ▷ C22×C139 ▷ C139 | |
| UCS | C1 ◁ C2×C4 ◁ C2×M16 | |
114 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=e,b^2=d,e^2=f,b^a=bd,g^a=g^138,c^b=cf,g^b=g^1381408 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804356, #31806676, #31806677, … |
| maximal normal subgroup of | #31804356, #31806676, #31806677, … |
| maximal quotient of | #31805176, #31805180, #31805185, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 577);