Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19127754 |
| Sylow | C83 ⋊ C2×#431 |
528 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293785, #35293786, #35293789, … |
| maximal normal subgroup of | #35293785, #35293786, #35293789, … |
| maximal quotient of | C2×#24907209, C2×C4×C22⋊(C83⋊C8), C2×C4×C4⋊(C83⋊C8), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13126);