Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4 |
No aliases for this group.
| Fitting | #384×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#127 |
924 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 924 conjugacy classes of subgroups — too many to draw. Only its 249 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=g,b^2=e,c^2=f,d^2=g,b^a=be,c^a=cf,h^d=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295343, #35295356, #35295369, … |
| maximal normal subgroup of | #35295343, #35295356, #35295369, … |
| maximal quotient of | #35325587, #384×Dic83, #35326191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7072);