Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×C4×C4⋊Dic83 |
| Sylow | C83 ⋊ C2×C4×C4⋊C4 |
928 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905302, C2×#24905303, #35293939, … |
| maximal normal subgroup of | C2×#24905302, C2×#24905303, #35293939, … |
| maximal quotient of | C2×C4×C83⋊#95, C42×C4⋊Dic83, C2×#24905690, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6845);