Finite Group DatabasebetaFinite Group Databasebeta| order | 10688 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C22×Q8×D167 |
| Fitting | C22×Q8×C167 ⋊ C2 |
| Sylow | C167 ⋊ C23×Q8 |
850 conjugacy classes of subgroups.
1700 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #36324060, #36324071, #391×D167, … |
| maximal normal subgroup of | #36324060, #36324071, #391×D167, … |
| maximal quotient of | C22×C4⋊C4×D167, C2×C4×Q8×D167, C22×#19128797, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10688, 1372);