Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #3046 |
472 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=e,d^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,d^b=dg,h^b=h^82,f^c=fg1180 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35442475, #35442480, #35442490, … |
| maximal normal subgroup of | #35442475, #35442480, #35442490, … |
| maximal quotient of | #35389868, #35389879, #35389890, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 14058);