C₅×D₂₁×C₁₆₇ #46856385

order	35070
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₂₁×C₁₆₇
unambiguous semidirect product	C₃⋊(C₅×D₇×C₁₆₇)
unambiguous semidirect product	C₇⋊(C₅×D₃×C₁₆₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₆₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₅×C₁₆₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₆₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₆₇

32 conjugacy classes of subgroups.

μ_t(G) = 17535

10020 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35070, 12);