Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C83 ⋊ C2 |
| Sylow | C83 ⋊ #2323 |
556 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^82,c^b=ce,h^c=h^821684 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35410140, #35410144, #35410170, … |
| maximal normal subgroup of | #35410140, #35410144, #35410170, … |
| maximal quotient of | #35325652, #35325697, #35325715, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7193);