Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C83 ⋊ C4×C4⋊C8 |
316 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 161 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=e,b^2=f,c^2=de,f^2=g,b^a=bd,h^c=h^821720 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35292340, #35292342, #35292348, … |
| maximal normal subgroup of | #35292340, #35292342, #35292348, … |
| maximal quotient of | #35295524, #35295528, #35295537, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4358);