Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#19128752 |
| Fitting | C2×C4⋊C4×C167 ⋊ C2 |
| Sylow | C167 ⋊ C2×#102 |
202 conjugacy classes of subgroups.
1688 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323952, C4×#19128752, #36323962, … |
| maximal normal subgroup of | #36323952, C4×#19128752, #36323962, … |
| maximal quotient of | C2×#24922996, #36322536, #36322562, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 535);