Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×#19127831 |
| Sylow | C83 ⋊ C2×#446 |
400 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 221 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 | #35294991, #35294993, #35295231, … |
| maximal normal subgroup of | #35294991, #35294993, #35295231, … |
| maximal quotient of | C2×#24907337, C2×#24907330, C4×#19127831, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13437);