Finite Group DatabasebetaFinite Group Databasebeta| order | 27380 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C37 |
No aliases for this group.
| Fitting, socle, derived, Hall | C5×C372 ⋊ C4 |
| Sylow | C372 ⋊ AGL(1,𝔽5) |
| Sylow | C5 ⋊ #19129959 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C372 | C4 |
| prime radical, cosocle | C5⋊(C37⋊D37) | C2 |
| LCS | G ▷ C5×C372 | |
| UCS | C1 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 370 |
Polycyclic presentation:
2^2,5,37^2|a^2=b,c^a=c^2,d^a=d^31,e^a=e^6,c^b=c^4,d^b=d^36,e^b=e^361715 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27380, 37);