Finite Group DatabasebetaFinite Group Databasebeta| order | 37926 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C9 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Hall | C72×C43 ⋊ C2×C9 |
| Hall | C7×#14582151 ⋊ C2 |
| Hall | C43×C7⋊D7 ⋊ C9 |
| Hall | C7⋊D7 ⋊ C43⋊C9 |
| Sylow | C72 ⋊ C2×C43⋊C9 |
| Sylow | C43 ⋊ (C7⋊C9)⋊D7 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C3 | #27162428 |
| commutator, hypocenter | C72×C43 | C2×C9 |
| Fitting, socle, cosocle | C3×C72×C43 | C2×C3 |
| prime radical | C3×C43×C7⋊D7 | C3 |
| LCS | G ▷ C72×C43 | |
| UCS | C1 ◁ C3 | |
64 conjugacy classes of subgroups.
| transitive degree | μt(G) = 2709 |
Polycyclic presentation:
2,3,7^2,43,3|b^3=f,c^a=c^6,d^a=d^6,c^b=c^2,e^b=e^361158 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(37926, 151);