Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#19127591 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#388 |
928 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35303236, #35303241, #35325559, … |
| maximal normal subgroup of | #35303236, #35303241, #35325559, … |
| maximal quotient of | C2×#24905689, C2×#24905695, C2×#24905699, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6941);