Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C22×#14581720 |
| Fitting | C22×C42×C83 ⋊ C2 |
| Sylow | C83 ⋊ C22×#104 |
856 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 856 conjugacy classes of subgroups — too many to draw. Only its 269 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 | #35309911, #35309917, #35309918, … |
| maximal normal subgroup of | #35309911, #35309917, #35309918, … |
| maximal quotient of | C22×#19127430, C22×#19127433, C2×#24905846, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13048);