Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C4×#14581839 |
| Fitting | C4×#41×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×2−1+4 |
1492 conjugacy classes of subgroups.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295806, #35295809, #35370789, … |
| maximal normal subgroup of | #35295806, #35295809, #35370789, … |
| maximal quotient of | C4×#19128181, C4×#19128180, C4×#19128184, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17720);