Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
| direct product | C4×#14581714 |
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 145 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 | #35295165, C8×#14581714, #35295179, … |
| maximal normal subgroup of | #35295165, C8×#14581714, #35295179, … |
| maximal quotient of | C4×#19127430, #35295027, #35295042, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4326);