Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | D4×C22⋊Dic83 |
| Sylow | C83 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
1690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35300821, #35300825, #35300849, … |
| maximal normal subgroup of | #35300821, #35300825, #35300849, … |
| maximal quotient of | C22⋊C4×C22⋊Dic83, C4⋊C4×C22⋊Dic83, D4×C83⋊#95, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7332);