Finite Group DatabasebetaFinite Group Databasebeta| order | 36417 |
| automorphism | ? |
| homology | Abelianization (H1) = C3 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C61×C199 ⋊ C3 |
| Sylow | C199 ⋊ C61⋊C3 |
| Sylow | C61 ⋊ C199⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C61×C199 | C3 |
| LCS | G ▷ C61×C199 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12139 |
Polycyclic presentation:
3,61,199|b^a=b^47,c^a=c^924049 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(36417, 4);