Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C210 |
| direct product | C22×C4⋊C4×D83 |
| Fitting | C22×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C23×C4⋊C4 |
2488 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 2488 conjugacy classes of subgroups — too many to draw. Only its 1157 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295732, #35309670, #35309680, … |
| maximal normal subgroup of | #35295732, #35309670, #35309680, … |
| maximal quotient of | C22×#95×D83, C2×C4×C4⋊C4×D83, C22×#19127552, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17669);