Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128248 |
| Fitting | C2×C4×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#532 |
1728 conjugacy classes of subgroups.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295782, #35370412, #35370531, … |
| maximal normal subgroup of | #35295782, #35370412, #35370531, … |
| maximal quotient of | C2×#24909867, C2×#24909924, C2×#24909926, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17790);