Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128237 |
| Fitting | C2×C22⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#529 |
1232 conjugacy classes of subgroups.
1204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295853, #35370387, #35370506, … |
| maximal normal subgroup of | #35295853, #35370387, #35370506, … |
| maximal quotient of | C2×#24909858, C2×#24909899, C2×#24909921, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17778);