Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C22×#14581787 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#126 |
1320 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1320 conjugacy classes of subgroups — too many to draw. Only its 565 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295767, #35297054, #35297056, … |
| maximal normal subgroup of | #35295767, #35297054, #35297056, … |
| maximal quotient of | C22×#19127568, C22×#19127582, C22×#19127584, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17767);