Finite Group DatabasebetaFinite Group Databasebeta| order | 18464 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C8×C577 ⋊ C2 |
| Sylow | C577 ⋊ #135 |
62 conjugacy classes of subgroups.
| transitive degree | μt(G) = 9232 |
Polycyclic presentation:
2^5,577|c^2=e,d^2=e,b^a=bd,d^a=de,f^a=f^576,d^b=de,f^b=f^5764622 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #49147755, #49147757, #49147758, … |
| maximal normal subgroup of | #49147755, #49147757, #49147758, … |
| maximal quotient of | #49147946, #49147987, C4×D4616, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18464, 168);