Finite Group DatabasebetaFinite Group Databasebeta| order | 29748 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C67 ⋊ C3×C4 |
| Hall | C67⋊#3866 ⋊ C3 |
| Hall | #21418334 ⋊ C4 |
| Sylow | C67 ⋊ #3866⋊C3 |
| Sylow | C37 ⋊ (C67⋊C3)⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C67 | C3×C4 |
| prime radical | #28415609 | C2 |
| cosocle | C67×D37 | C2×C3 |
| LCS | G ▷ C37×C67 | |
| UCS | C1 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2479 |
Polycyclic presentation:
2,3,2,37,67|a^2=c,d^a=d^31,e^a=e^66,d^b=d^26,e^b=e^37,d^c=d^36235 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29748, 28);