C₅×C₁₃×C₃⋊D₃ #11924070

order	1170
isoclinism	isoclinic class of C₃⋊D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₃ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₅×C₁₃×C₃⋊D₃
unambiguous semidirect product	C₃⋊(C₅×D₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₅×C₁₃	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂×C₅×C₁₃
Frattini	C₁	G
Fitting, socle	C₃²×C₅×C₁₃	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₅×C₁₃

48 conjugacy classes of subgroups.

minimal degree	μ(G) = 24
transitive degree	μ_t(G) = 585

A minimal faithful permutation representation — 3 generators on 24 points:

(1,2,3,4,5)(6,7,8,9,10,11,12,13,14,15,16,17,18)(20,21)(23,24);(22,23,24);(19,20,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1170, 28);