Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127778 |
| Fitting | C2×C4⋊C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#436 |
552 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 213 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 | #35294981, #35294983, #35295221, … |
| maximal normal subgroup of | #35294981, #35294983, #35295221, … |
| maximal quotient of | C2×#24906347, C2×#24906352, C2×#24906359, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13196);