Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25×C4 |
| direct product | C2×#19128078 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#493 |
760 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 760 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.
2668 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35299680, #35303648, #35303650, … |
| maximal normal subgroup of | #35299680, #35303648, #35303650, … |
| maximal quotient of | C2×#24907055, C2×#24907069, C2×#24907078, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14922);