Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | C22×C42×C83 ⋊ C2 |
| Sylow | C83 ⋊ #1437 |
828 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 828 conjugacy classes of subgroups — too many to draw. Only its 241 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,c^2=ef,b^a=bd,c^a=ce,h^a=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295916, #1437×D83, C2×#24905701, … |
| maximal normal subgroup of | #35295916, #1437×D83, C2×#24905701, … |
| maximal quotient of | #35292324, #35292325, #35292327, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 2748);