Finite Group DatabasebetaFinite Group Databasebeta| order | 10624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Sylow | C83 ⋊ #2365 |
552 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,83|a^2=g,b^2=g,c^2=f,d^2=e,b^a=be,c^a=cf,d^b=de,h^c=h^821690 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35426654, #35426656, #35426676, … |
| maximal normal subgroup of | #35426654, #35426656, #35426676, … |
| maximal quotient of | C4⋊C4×Dic83⋊C4, #35325942, #35325945, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10624, 7564);