Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128174 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#518 |
1920 conjugacy classes of subgroups.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309745, #35309748, #35309790, … |
| maximal normal subgroup of | #35309745, #35309748, #35309790, … |
| maximal quotient of | C2×#24909815, C2×#24909816, C2×#24909818, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17695);