Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C22×#14581933 |
| Fitting | C22×C8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C22×M16 |
298 conjugacy classes of subgroups.
2696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36323830, #36323833, #36323856, … |
| maximal normal subgroup of | #36323830, #36323833, #36323856, … |
| maximal quotient of | C22×#19128742, C2×C4×#14581933, C22×(C2×D167)⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1308);