Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Sylow | C83 ⋊ #2369 |
496 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=fg,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^b=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35298860, #35298862, #35298864, … |
| maximal normal subgroup of | #35298860, #35298862, #35298864, … |
| maximal quotient of | C4⋊C4×C4⋊Dic83, #35325949, #35325953, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7599);