C₅×C₃⋊(C₃⋊(C₃⋊Dic₃)) #13108509

order	1620
isoclinism	isoclinic class of C₃⋊(C₃⋊(C₃⋊D₃))
automorphism	?
homology	Abelianization (H₁) = C₄×C₅ · Schur multiplier (H₂) = C₃⁶

Aliases

direct product	C₅×C₃⋊(C₃⋊(C₃⋊Dic₃))
unambiguous semidirect product	C₃⋊(C₅×C₃⋊(C₃⋊Dic₃))

derived, Sylow	C₃⁴ ⋊ C₄×C₅
Hall	C₃⁴×C₅ ⋊ C₄

1272 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 1620

A minimal faithful permutation representation — 5 generators on 21 points:

(1,2,3,4,5)(6,7,8,9)(11,12)(14,15)(17,18)(20,21);(19,20,21);(16,17,18);(13,14,15);(10,11,12)

420 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 415);