Finite Group DatabasebetaFinite Group Databasebeta| order | 21372 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C3⋊#20297117 |
| Fitting, socle, derived, Hall | C3×C13×C137 ⋊ C4 |
| Hall | C13×C137 ⋊ Dic3 |
| Hall | C3×C137 ⋊ #261 |
| Sylow | C137 ⋊ C3⋊#261 |
| Hall | C3×C13 ⋊ #10587739 |
| Sylow | C13 ⋊ C3⋊#10587739 |
| Sylow | C3 ⋊ #20297117 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C3×C13×C137 | C4 |
| prime radical, cosocle | C3×D1781 | C2 |
| LCS | G ▷ C3×C13×C137 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5343 |
Polycyclic presentation:
2^2,3,13,137|a^2=b,c^a=c^2,d^a=d^5,e^a=e^100,d^b=d^12,e^b=e^1361341 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(21372, 34);