Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
| direct product | C2×#19128312 |
| Fitting | C2×C4⋊Q8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#541 |
1004 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1004 conjugacy classes of subgroups — too many to draw. Only its 485 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35296945, #35409558, #35409683, … |
| maximal normal subgroup of | #35296945, #35409558, #35409683, … |
| maximal quotient of | C2×#24910071, C2×#24910108, C2×#24910148, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 17877);