Finite Group DatabasebetaFinite Group Databasebeta| order | 37164 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C19×C163 ⋊ C3×C4 |
| Hall | Dic3097 ⋊ C3 |
| Hall | #22604696 ⋊ C4 |
| Sylow | C163 ⋊ (C19⋊C3)⋊C4 |
| Sylow | C19 ⋊ (C163⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | #32915721 |
| commutator, hypocenter | C19×C163 | C3×C4 |
| Fitting, socle, cosocle | C2×C19×C163 | C2×C3 |
| prime radical | C2×#22604696 | C2 |
| LCS | G ▷ C19×C163 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12388 |
Polycyclic presentation:
2,3,19,163,2|a^2=e,c^a=c^18,d^a=d^162,c^b=c^7,d^b=d^1041044 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37164, 23);