Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | C2×#19127819 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#443 |
472 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
2680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#24905435, C2×#24905437, #35314190, … |
| maximal normal subgroup of | C2×#24905435, C2×#24905437, #35314190, … |
| maximal quotient of | C2×C8×D664, C2×C8×#13050579, C2×C8×Dic332, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13401);