C₅×C₁₇×AGL(1,𝔽₇) #16813192

order	3570
isoclinism	isoclinic class of AGL(1,𝔽₇)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×C₁₇×AGL(1,𝔽₇)
unambiguous semidirect product	D₇⋊(C₃×C₅×C₁₇)
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₂×C₅×C₁₇)
unambiguous semidirect product	(C₅×D₇)⋊(C₃×C₁₇)
unambiguous semidirect product	(D₇×C₁₇)⋊(C₃×C₅)
unambiguous semidirect product	(C₅×D₇×C₁₇)⋊C₃

	subgroup	G/H
center, hypercenter	C₅×C₁₇	AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₇	C₂×C₃×C₅×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇	C₂×C₃
LCS	G ▷ C₇
UCS	C₁ ◁ C₅×C₁₇

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 595

A minimal faithful permutation representation — 2 generators on 29 points:

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3570, 19);