Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42 |
| direct product | C4×#14581750 |
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#117 |
752 conjugacy classes of subgroups.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35293930, #35293934, #35293978, … |
| maximal normal subgroup of | #35293930, #35293934, #35293978, … |
| maximal quotient of | C4×#19127546, C4×#19127548, C4×C4⋊C4×Dic83, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6850);