Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×C4×#13050589 |
| Fitting | C2×C4×D4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×C4×#41 |
1728 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295777, #35370212, #35370214, … |
| maximal normal subgroup of | #35295777, #35370212, #35370214, … |
| maximal quotient of | C2×C4×#14581748, C2×C4×#14581750, C2×C4×(C22⋊D83)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17688);