D₇×C₁₇×C₁₉ #17985286

order	4522
isoclinism	isoclinic class of D₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₇×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇×C₁₇×C₁₉
unambiguous semidirect product	C₇⋊(C₂×C₁₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₁₇×C₁₉	D₇
commutator, cosocle, hypocenter	C₇	C₂×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₇
UCS	C₁ ◁ C₁₇×C₁₉

16 conjugacy classes of subgroups.

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2261

A minimal faithful permutation representation — 2 generators on 43 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)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(2,7)(3,6)(4,5)

1615 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4522, 5);