Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Fitting | D4×C577 ⋊ C4 |
| Sylow | C577 ⋊ #104 |
44 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=d,c^2=e,d^2=e,b^a=bc,c^a=ce,f^a=f^553,c^b=ce,f^d=f^576734 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#32914728, D577⋊#104, #49148946, … |
| maximal normal subgroup of | C2×#32914728, D577⋊#104, #49148946, … |
| maximal quotient of | D4⋊#17987237, #49148799, #49148800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 210);