Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C4×C8×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2922 |
400 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 181 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,c^2=e,f^2=g,b^a=be,d^b=dg,h^b=h^822680 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35295094, #35295096, #35295099, … |
| maximal normal subgroup of | #35295094, #35295096, #35295099, … |
| maximal quotient of | #35401888, C4×#19127667, C4×#19127727, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13152);