Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C137 ⋊ C2 |
| Sylow | C137 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D137 |
| commutator, socle | C2×C137 | C2×C16 |
| Fitting | C32×C137 | C2 |
| hypercenter | C32 | D137 |
| hypocenter | C137 | M64 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C16 ◁ C32 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^b=g^1362216 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M64×D137, C2×#22577236, #31783082, … |
| maximal normal subgroup of | M64×D137, C2×#22577236, #31783082, … |
| maximal quotient of | #31778922, #31778926, #31778984, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 382);