Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C2 |
| direct product | C2×C167⋊C32 |
| unambiguous semidirect product | (C2×C167)⋊C32 |
| derived, Sylow | C167 ⋊ C2×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D167 |
| commutator, hypocenter | C167 | C2×C32 |
| Frattini | C16 | C2×D167 |
| Fitting | C2×C16×C167 | C2 |
| socle, prime radical | C22×C167 | C16 |
| cosocle | C16×C167 | C22 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C2×C16 | |
34 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C32×Dic167, C4×C167⋊C32, #36322271, … |
| maximal normal subgroup of | C32×Dic167, C4×C167⋊C32, #36322271, … |
| maximal quotient of | C4×C167⋊C32, C22⋊(C167⋊C32), C4⋊(C167⋊C32), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 381);