Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
| direct product | #125×D167 |
| Fitting | #125×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#125 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D167 |
| commutator, socle, cosocle | C22×C167 | C24 |
| Fitting | #125×C167 | C2 |
| prime radical | C22×D167 | C23 |
| hypercenter | #125 | D167 |
| hypocenter | C167 | C2×#125 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C22 ◁ #125 | |
226 conjugacy classes of subgroups.
1190 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #330×D167, #36322738, #36322763, … |
| maximal normal subgroup of | #330×D167, #36322738, #36322763, … |
| maximal quotient of | #382×D167, #387×D167, #389×D167, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1068);