Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128182 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#520 |
1640 conjugacy classes of subgroups.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309840, #35309884, #35309920, … |
| maximal normal subgroup of | #35309840, #35309884, #35309920, … |
| maximal quotient of | C2×#24909817, C2×#24909820, C2×#24909821, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17705);