Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C211 |
| direct product | C23×C22⋊Dic83 |
| Sylow | C83 ⋊ C23×C22⋊C4 |
4632 conjugacy classes of subgroups.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292326, #35309665, #35309701, … |
| maximal normal subgroup of | #35292326, #35309665, #35309701, … |
| maximal quotient of | C23×C83⋊#95, C22×C4×C22⋊Dic83, C22×#19127557, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17668);