Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C29 |
| direct product | C2×#19127556 |
| Fitting | C22×C22⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ C2×#379 |
3464 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 3464 conjugacy classes of subgroups — too many to draw. Only its 429 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 | #35309664, #35309700, #35310721, … |
| maximal normal subgroup of | #35309664, #35309700, #35310721, … |
| maximal quotient of | C2×(C2×D83)⋊#95, C2×#24905685, C4×#19127556, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6877);