Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Sylow | C137 ⋊ H(3,ℤ/4) |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C4×Dic137 |
| commutator | C4×C137 | C42 |
| Frattini | C22×C4 | C2×D137 |
| Fitting | #117×C137 | C2 |
| socle | C2×C137 | #95 |
| hypercenter | #117 | D137 |
| hypocenter | C137 | H(3,ℤ/4) |
| LCS | G ▷ C4×C137 ▷ C137 | |
| UCS | C1 ◁ C4 ◁ #117 | |
94 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=d,b^2=e,c^2=f,b^a=bc,e^a=ef,d^b=df,g^b=g^1361382 conjugacy classes. The character table is too large to display.
| maximal subgroup of | H(3,ℤ/4)×D137, C2×#22577159, #31780543, … |
| maximal normal subgroup of | H(3,ℤ/4)×D137, C2×#22577159, #31780543, … |
| maximal quotient of | #31778617, #31778618, #31778619, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 305);