Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C32×D167 |
| Fitting | C32×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C32 | D167 |
| commutator, hypocenter | C167 | C2×C32 |
| Frattini | C16 | C2×D167 |
| Fitting | C32×C167 | C2 |
| socle | C2×C167 | C2×C16 |
| prime radical | C2×D167 | C16 |
| cosocle | C16×C167 | C22 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C32 | |
34 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C64×D167, #36322348, C2×C32×D167, … |
| maximal normal subgroup of | C64×D167, #36322348, C2×C32×D167, … |
| maximal quotient of | C32×Dic167, (C2×D167)⋊C32, Dic167⋊C32, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 380);