Finite Group DatabasebetaFinite Group Databasebeta| order | 18507 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C31×C199 ⋊ C3 |
| Sylow | C199 ⋊ C31⋊C3 |
| Sylow | C31 ⋊ C199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C31×C199 | C3 |
| LCS | G ▷ C31×C199 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6169 |
Polycyclic presentation:
3,31,199|b^a=b^5,c^a=c^922059 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#32915019, #49149924, #49149928, … |
| maximal normal subgroup of | C2×#32915019, #49149924, #49149928, … |
| maximal quotient of | C2×#32915019 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(18507, 3);