C₇×C₅⋊(C₁₇⋊AGL(1,𝔽₇)) #38735960

order	24990
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₅⋊(C₁₇⋊AGL(1,𝔽₇))
unambiguous semidirect product	C₅⋊(C₇×C₁₇⋊AGL(1,𝔽₇))
unambiguous semidirect product	C₁₇⋊(C₇×C₅⋊AGL(1,𝔽₇))
unambiguous semidirect product	ΓL(1,𝔽₈)⋊(C₇×D₈₅)
unambiguous semidirect product	D₅₉₅⋊(C₃×C₇)

	subgroup	G/H
center, hypercenter	C₇	C₅⋊(C₁₇⋊AGL(1,𝔽₇))
commutator, cosocle, hypocenter	C₅×C₇×C₁₇	C₂×C₃×C₇
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₁₇	C₂×C₃
LCS	G ▷ C₅×C₇×C₁₇
UCS	C₁ ◁ C₇

68 conjugacy classes of subgroups.

μ_t(G) = 3570

1519 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24990, 50);