Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| isoclinism | isoclinic class of D167 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C23×C4×D167 |
| Fitting | C23×C4×C167 ⋊ C2 |
| derived, Sylow | C167 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C4 | D167 |
| commutator, hypocenter | C167 | C24×C4 |
| Frattini | C2 | C24×D167 |
| Fitting | C23×C4×C167 | C2 |
| socle | C24×C167 | C22 |
| prime radical | C24×D167 | C2 |
| cosocle | C2×C167 | C25 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C23×C4 | |
1362 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D167)⋊#95, #36324047, C2×#95×D167, … |
| maximal normal subgroup of | (C2×D167)⋊#95, #36324047, C2×#95×D167, … |
| maximal quotient of | C22×C42×D167, C23×C4×Dic167, C22×C22⋊C4×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1367);