C₂×C₁₃×C₅²⋊C₃ #14519617

order	1950
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₂×C₁₃×C₅²⋊C₃
unambiguous semidirect product	(C₂×C₅²)⋊(C₃×C₁₃)

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

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 390

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2)(3,4,5,6,7,8,9,10,11,12,13,14,15)(16,17,19)(18,22,24)(20,25,28)(21,27,30)(23,26,29);(16,18,23,28,30)(17,22,26,20,21)(19,25,24,27,29)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 27);