Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
| direct product | C2×#19128093 |
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#497 |
564 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299340, #35305699, #35305700, … |
| maximal normal subgroup of | #35299340, #35305699, #35305700, … |
| maximal quotient of | C2×#24907088, C2×#24907095, C2×#24907107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14948);