C₅²×D₃₉ #14519625

order	1950
isoclinism	isoclinic class of D₃₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₅² · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃₉
unambiguous semidirect product	C₃⋊(C₅²×D₁₃)
unambiguous semidirect product	C₁₃⋊(C₅²×D₃)

	subgroup	G/H
center, hypercenter	C₅²	D₃₉
commutator, cosocle, hypocenter	C₃×C₁₃	C₂×C₅²
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₁₃	C₂
LCS	G ▷ C₃×C₁₃
UCS	C₁ ◁ 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)(11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26);(6,7,8,9,10)(12,13)(15,26)(16,25)(17,24)(18,23)(19,22)(20,21)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1950, 35);