Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C16 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C32×C167 ⋊ C2 |
| Sylow | C167 ⋊ M64 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C16 | C2×D167 |
| commutator, socle | C2×C167 | C2×C16 |
| Fitting | C32×C167 | C2 |
| prime radical | C2×D167 | C16 |
| cosocle | C16×C167 | C22 |
| hypercenter | C32 | D167 |
| hypocenter | C167 | M64 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C16 ◁ C32 | |
32 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,167|a^2=c,c^2=d,d^2=e,e^2=f,b^a=bf,g^b=g^1662696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M64×D167, C2×#24923102, #36326431, … |
| maximal normal subgroup of | M64×D167, C2×#24923102, #36326431, … |
| maximal quotient of | #36322271, (C2×D167)⋊C32, Dic167⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 382);