C₁₃×C₃⋊(C₅⋊D₅) #14519628

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

Aliases

direct product	C₁₃×C₃⋊(C₅⋊D₅)
unambiguous semidirect product	C₃⋊(C₁₃×C₅⋊D₅)
unambiguous semidirect product	C₅⋊(C₁₃×D₁₅)

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊(C₅⋊D₅)
commutator, cosocle, hypocenter	C₃×C₅²	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃	C₂
LCS	G ▷ C₃×C₅²
UCS	C₁ ◁ 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)(15,16)(18,19)(20,21)(23,24)(25,26);(14,15,16)(22,23,25,26,24);(17,18,20,21,19)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 38);