Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C4×#14581719 |
| Sylow | C83 ⋊ C4×#104 |
360 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 133 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
1696 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14581719, #35295115, #35295117, … |
| maximal normal subgroup of | C8×#14581719, #35295115, #35295117, … |
| maximal quotient of | C4×D4⋊(C83⋊C8), C4×Q8⋊(C83⋊C8), #35295016, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4315);