Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | C2×C4×C577 ⋊ C4 |
| Sylow | C577 ⋊ #117 |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4616 |
Polycyclic presentation:
2^5,577|a^2=e,c^2=d,b^a=bd,f^a=f^553,f^e=f^5761172 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49148816, #49148817, #49148820, … |
| maximal normal subgroup of | #49148816, #49148817, #49148820, … |
| maximal quotient of | #49148885, C4×C22⋊#14556313, C4×C4⋊#14556313, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 225);