C₁₉×D₆₃ #14558797

order	2394
isoclinism	isoclinic class of D₆₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×D₆₃
unambiguous semidirect product	C₇⋊(D₉×C₁₉)
unambiguous semidirect product	C₉⋊(D₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₉	D₆₃
commutator, cosocle, hypocenter	C₇×C₉	C₂×C₁₉
Frattini	C₃	C₁₉×D₂₁
Fitting	C₇×C₉×C₁₉	C₂
socle	C₃×C₇×C₁₉	D₃
LCS	G ▷ C₇×C₉
UCS	C₁ ◁ C₁₉

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 1197

A minimal faithful permutation representation — 2 generators on 35 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23,24,25,26,27,28)(29,30,31,32,33,34,35);(21,28)(22,27)(23,26)(24,25)(30,35)(31,34)(32,33)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2394, 23);