Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#17987237 |
| Sylow | C577 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 18464 |
Polycyclic presentation:
2^5,577|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^553,f^d=f^5761172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#17987237, #49148797, Q8⋊#17987237, … |
| maximal normal subgroup of | D4⋊#17987237, #49148797, Q8⋊#17987237, … |
| maximal quotient of | #49148810, #49148812, #49148815, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 212);