Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | #340×C83 ⋊ C2 |
| Sylow | C83 ⋊ C4×#102 |
396 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 129 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=e,d^2=g,f^2=g,b^a=bd,d^a=dg,f^a=fg,h^c=h^821204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×#102×D83, C2×#24907277, #35402153, … |
| maximal normal subgroup of | C4×#102×D83, C2×#24907277, #35402153, … |
| maximal quotient of | #35294995, #35295025, #35295040, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 4324);