Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C210 |
| direct product | C23×C22⋊D167 |
| Fitting | C25×C167 ⋊ C2 |
| Sylow | C167 ⋊ C23×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C24 | C2×D167 |
| commutator, cosocle | C2×C167 | C25 |
| Frattini | C2 | C24×D167 |
| Fitting | C25×C167 | C2 |
| socle | C24×C167 | C22 |
| hypercenter | C25 | D167 |
| hypocenter | C167 | C23×D4 |
| LCS | G ▷ C2×C167 ▷ C167 | |
| UCS | C1 ◁ C24 ◁ C25 | |
1362 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322377, #36324052, C2×#24923145, … |
| maximal normal subgroup of | #36322377, #36324052, C2×#24923145, … |
| maximal quotient of | C23×(C2×D167)⋊C4, C23×C22⋊Dic167, C23×Dic167⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1370);