Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
| direct product | C22×#14581713 |
| Sylow | C83 ⋊ C22×#102 |
1072 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 1072 conjugacy classes of subgroups — too many to draw. Only its 389 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 | #35309968, #35309970, #35310666, … |
| maximal normal subgroup of | #35309968, #35309970, #35310666, … |
| maximal quotient of | C22×D4⋊(C83⋊C8), C2×#24905888, C2×#24905862, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 12996);