Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19127753 |
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293861, #35293864, #35293882, … |
| maximal normal subgroup of | #35293861, #35293864, #35293882, … |
| maximal quotient of | C2×#24907207, C2×#24907220, C2×C4⋊C8×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13125);