Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#19128750 |
| Sylow | C167 ⋊ C2×#101 |
146 conjugacy classes of subgroups.
1682 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323933, C4×#19128750, #36324060, … |
| maximal normal subgroup of | #36323933, C4×#19128750, #36324060, … |
| maximal quotient of | C2×#24922994, #36322461, #36322467, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 528);