Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#19128176 |
| Sylow | C83 ⋊ C2×#518 |
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1708 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35309721, #35309724, #35309746, … |
| maximal normal subgroup of | #35309721, #35309724, #35309746, … |
| maximal quotient of | C2×#24909816, C2×#24909820, C2×#24909824, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17697);