Finite Group DatabasebetaFinite Group Databasebeta| order | 37518 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C13 |
No aliases for this group.
| Fitting, socle, derived, Hall | C132×C37 ⋊ C2×C3 |
| Hall | C37⋊#92789 ⋊ C2 |
| Hall | C13⋊D481 ⋊ C3 |
| Sylow | C132 ⋊ D37⋊C3 |
| Sylow | C37 ⋊ #11759816 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C132×C37 | C2×C3 |
| LCS | G ▷ C132×C37 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
| minimal degree | μ(G) = 63 |
| transitive degree | μt(G) = 1443 |
A minimal faithful permutation representation — 2 generators on 63 points:
(2,6,7,3,4,8)(5,12,11,9,10,13)(15,19,20,16,17,21)(18,24,25,22,23,26)(28,32,33,29,30,34)(31,40,41,35,36,49)(37,52,53,43,44,60)(38,51,47,45,42,39)(46,62,63,55,54,58)(48,50,61,57,56,59);(1,2,5,4,8,11,10,12,13,7,6,9,3)(14,15,18,20,19,23,25,26,24,17,21,22,16)(27,28,31,37,44,54,59,60,57,47,33,32,38,46,56,36,42,49,58,63,41,51,40,50,55,45,30,34,39,48,53,61,62,52,43,35,29)Polycyclic presentation:
2,3,13^2,37|c^a=c^12,d^a=d^12,e^a=e^36,c^b=c^3,d^b=d^9,e^b=e^261048 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37518, 76);