Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | #431×D83 |
| Fitting | #431×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 | #1274×D83, #35293801, #35293810, … |
| maximal normal subgroup of | #1274×D83, #35293801, #35293810, … |
| maximal quotient of | #1744×D83, C4×C22⋊C8×D83, C4×C4⋊C8×D83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13122);