Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C24×Dic167 |
| derived, Sylow | C167 ⋊ C24×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C25 | D167 |
| commutator, hypocenter | C167 | C24×C4 |
| Frattini | C2 | C24×D167 |
| Fitting, socle, prime radical | C25×C167 | C2 |
| cosocle | C2×C167 | C25 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C25 | |
1362 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36322360, C22×C167⋊#95, C2×C22⋊C4×Dic167, … |
| maximal normal subgroup of | #36322360, C22×C167⋊#95, C2×C22⋊C4×Dic167, … |
| maximal quotient of | C23×C4×Dic167, C23×C22⋊Dic167, C23×C4⋊Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1368);