Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C25 |
| direct product | #336×D83 |
| Fitting | #336×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#336 |
528 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 528 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.
1720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #1270×D83, #1271×D83, #1272×D83, … |
| maximal normal subgroup of | #1270×D83, #1271×D83, #1272×D83, … |
| maximal quotient of | #1273×D83, #35293784, #35293788, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4199);