Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2947 |
470 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=f,b^2=g,c^2=f,e^2=g,b^a=be,e^a=eg,h^a=h^82,e^b=eg,h^b=h^82,d^c=dg,h^c=h^821192 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35425197, #35425200, #35425215, … |
| maximal normal subgroup of | #35425197, #35425200, #35425215, … |
| maximal quotient of | #35373856, #35374047, #35374060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 13356);