Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C43 · Schur multiplier (H2) = C43 |
| direct product | C42×Dic167 |
| unambiguous semidirect product | C167⋊C43 |
| derived, Sylow | C167 ⋊ C43 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C42 | D167 |
| commutator, hypocenter | C167 | C43 |
| Frattini | C23 | C22×D167 |
| Fitting | C2×C42×C167 | C2 |
| socle, prime radical, cosocle | C23×C167 | C23 |
| LCS | G ▷ C167 | |
| UCS | C1 ◁ C2×C42 | |
258 conjugacy classes of subgroups.
2720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36321970, C4×C8×Dic167, #97×Dic167, … |
| maximal normal subgroup of | #36321970, C4×C8×Dic167, #97×Dic167, … |
| maximal quotient of | #95×Dic167, C4×C167⋊#95, C4×C8×Dic167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 391);