Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#19128829 |
| Fitting | C2×C42×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#127 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C22×D167 |
| commutator, cosocle | C22×C167 | C24 |
| Frattini | C22 | C23×D167 |
| Fitting | C2×C42×C167 | C2 |
| socle | C23×C167 | C23 |
| hypercenter | C2×C42 | D167 |
| hypocenter | C167 | C2×#127 |
| LCS | G ▷ C22×C167 ▷ C167 | |
| UCS | C1 ◁ C23 ◁ C2×C42 | |
498 conjugacy classes of subgroups.
2684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24923012, #36322805, #36322807, … |
| maximal normal subgroup of | C2×#24923012, #36322805, #36322807, … |
| maximal quotient of | C2×#24923139, C2×#24923171, C4×#19128829, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1089);