Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | #356×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2135 |
230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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=g,c^2=g,d^2=g,e^2=g,b^a=bd,d^a=df,f^a=fg,c^b=cg,d^b=dg,e^b=efg,h^c=h^82,e^d=eg556 conjugacy classes — view the full character table.
| maximal subgroup of | #35324817, #35324819, #35324822, … |
| maximal normal subgroup of | #35324817, #35324819, #35324822, … |
| maximal quotient of | #35313518, #35313570, #35313695, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 6203);