Finite Group DatabasebetaFinite Group Databasebeta| order | 8896 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C139 ⋊ #347 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic139 |
| commutator | C4×C139 | C42 |
| Frattini | C2×C8 | C2×D139 |
| Fitting | #97×C139 | C2 |
| socle | C2×C139 | #97 |
| hypercenter | #97 | D139 |
| hypocenter | C139 | #347 |
| LCS | G ▷ C4×C139 ▷ C139 | |
| UCS | C1 ◁ C4 ◁ #97 | |
46 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,139|a^2=c,b^2=d,c^2=e,e^2=f,b^a=be,d^a=df,g^a=g^138,c^b=cf1402 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31804436, #31804437, #31804438, … |
| maximal normal subgroup of | #31804436, #31804437, #31804438, … |
| maximal quotient of | #31804325, #31804484, C2×#22580731 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8896, 327);