Finite Group DatabasebetaFinite Group Databasebeta| order | 19188 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, socle, derived, Hall | C32×C13×C41 ⋊ C4 |
| Hall | C13×C41 ⋊ #157 |
| Hall | C32×C41 ⋊ #261 |
| Hall | C32×C13 ⋊ #4223 |
| Sylow | C41 ⋊ #90866 |
| Sylow | C13 ⋊ #13093287 |
| Sylow | C32 ⋊ #14523821 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C32×C13×C41 | C4 |
| prime radical, cosocle | C3⋊D1599 | C2 |
| LCS | G ▷ C32×C13×C41 | |
| UCS | C1 | |
40 conjugacy classes of subgroups.
| transitive degree | μt(G) = 3198 |
Polycyclic presentation:
2^2,3^2,13,41|a^2=b,c^a=cd,d^a=cd^2,e^a=e^5,f^a=f^32,c^b=c^2,d^b=d^2,e^b=e^12,f^b=f^401203 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19188, 146);