Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C28 |
| direct product | C2×#19127610 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#392 |
1812 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 277 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299411, #35299413, #35299426, … |
| maximal normal subgroup of | #35299411, #35299413, #35299426, … |
| maximal quotient of | C2×#24905702, C2×#24905703, C2×#24905707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7706);