Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C139 ⋊ #346 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C2×D139 |
| commutator | C2×C139 | C4×C8 |
| Fitting | C2×C16×C139 | C2 |
| socle | C22×C139 | C2×C8 |
| hypercenter | C2×C16 | D139 |
| hypocenter | C139 | #346 |
| LCS | G ▷ C2×C139 ▷ C139 | |
| UCS | C1 ◁ C2×C8 ◁ C2×C16 | |
54 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=c,b^2=d,c^2=e,e^2=f,b^a=bf,g^b=g^1382248 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804539, #346×D139, C2×#22580728, … |
| maximal normal subgroup of | #31804539, #346×D139, C2×#22580728, … |
| maximal quotient of | #31804320, #31804323, #31804481, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 324);