Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C577 ⋊ M32 |
26 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|a^2=c,c^2=d,d^2=e,b^a=be,f^a=f^553,f^c=f^5761172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148841, #49148842, #49148845, … |
| maximal normal subgroup of | #49148841, #49148842, #49148845, … |
| maximal quotient of | #49148837, C22⋊#22604421, C4⋊#22604421, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 220);