C₃×C₁₃×C₅⋊D₅ #14519622

order	1950
isoclinism	isoclinic class of C₅⋊D₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₃×C₁₃×C₅⋊D₅
unambiguous semidirect product	C₅⋊(C₃×D₅×C₁₃)

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃×C₁₃

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 975

A minimal faithful permutation representation — 3 generators on 26 points:

(1,2,3)(4,5,6,7,8,9,10,11,12,13,14,15,16)(18,19)(20,21)(23,24)(25,26);(22,23,25,26,24);(17,18,20,21,19)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 32);