Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×C16×D167 |
| Fitting | C2×C16×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C16 | D167 |
| commutator, hypocenter | C167 | C22×C16 |
| Frattini | C8 | C22×D167 |
| Fitting | C2×C16×C167 | C2 |
| socle | C22×C167 | C2×C8 |
| prime radical | C22×D167 | C8 |
| cosocle | C8×C167 | C23 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C2×C16 | |
98 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D167)⋊C32, C4×C16×D167, #346×D167, … |
| maximal normal subgroup of | (C2×D167)⋊C32, C4×C16×D167, #346×D167, … |
| maximal quotient of | C4×C16×D167, C2×C16×Dic167, C22⋊C16×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 960);