C₃×C₅²×D₁₃ #14519619

order	1950
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅² · Schur multiplier (H₂) = C₅

Aliases

C₃×C₅²×D₁₃

	subgroup	G/H
center, hypercenter	C₃×C₅²	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₅²

64 conjugacy classes of subgroups.

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

A minimal faithful permutation representation — 2 generators on 26 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 29);