C₁₇×C₅⋊AGL(1,𝔽₇) #16813196

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

Aliases

direct product	C₁₇×C₅⋊AGL(1,𝔽₇)
unambiguous semidirect product	C₅⋊(C₁₇×AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(D₅×C₁₇)
unambiguous semidirect product	D₃₅⋊(C₃×C₁₇)
unambiguous semidirect product	(C₁₇×D₃₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₁₇	C₅⋊AGL(1,𝔽₇)
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₃×C₁₇
Frattini	C₁	G
Fitting, socle	C₅×C₇×C₁₇	C₂×C₃
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ 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)(19,20)(21,22)(24,27,28,25,26,29);(18,19,21,22,20)(23,24,26,29,28,27,25)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3570, 23);