C₁₃×(C₅⋊D₅)⋊C₃ #14519612

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

Aliases

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

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

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 28
transitive degree	μ_t(G) = 195

A minimal faithful permutation representation — 2 generators on 28 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17)(16,19,23,20,18,25)(21,26,28,27,24,22);(14,16,21,27,20)(15,18,24,26,19)(17,22,23,25,28)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 22);