Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C22⋊C4×C577 ⋊ C2 |
| Sylow | C577 ⋊ C4×D4 |
94 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|a^2=e,c^2=e,b^a=bd,f^c=f^5762900 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D4×D577, C2×#32914624, C4×#22604417, … |
| maximal normal subgroup of | C4×D4×D577, C2×#32914624, C4×#22604417, … |
| maximal quotient of | #49147796, C22⋊C4×Dic577, #49147800, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 106);