Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C25 |
| direct product | #41×C83⋊C8 |
| Sylow | C83 ⋊ C8×#41 |
456 conjugacy classes of subgroups; only the 305 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 305 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 | #104×C83⋊C8, #35295115, #35295120, … |
| maximal normal subgroup of | #104×C83⋊C8, #35295115, #35295120, … |
| maximal quotient of | #117×C83⋊C8, C4×D4×C83⋊C8, C4×Q8×C83⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13469);