C₂²×C₁₃×C₅²⋊C₃ #16839192

order	3900
isoclinism	isoclinic class of C₅²⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₁₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

C₂²×C₁₃×C₅²⋊C₃

	subgroup	G/H
center, hypercenter	C₂²×C₁₃	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₂²×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₁₃	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂²×C₁₃

60 conjugacy classes of subgroups.

minimal degree	μ(G) = 32
transitive degree	μ_t(G) = 780

A minimal faithful permutation representation — 2 generators on 32 points:

(1,2)(5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21)(20,24,26)(22,27,30)(23,29,32)(25,28,31);(3,4)(18,20,25,30,32)(19,24,28,22,23)(21,27,26,29,31)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3900, 200);