Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4 |
| direct product | C42×D332 |
| Fitting | C43×C83 ⋊ C2 |
| Sylow | C83 ⋊ C42×D4 |
924 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#19127430, C4×#19127428, #35295007, … |
| maximal normal subgroup of | C4×#19127430, C4×#19127428, #35295007, … |
| maximal quotient of | C42×(C2×D83)⋊C4, C42×C4⋊Dic83, C4×#19127579, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6858);