C₅×D₃×C₇×C₁₅₇ #45682129

order	32970
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇×C₁₅₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃×C₇×C₁₅₇
unambiguous semidirect product	C₃⋊(C₂×C₅×C₇×C₁₅₇)

	subgroup	G/H
center, hypercenter	C₅×C₇×C₁₅₇	D₃
commutator, cosocle, hypocenter	C₃	C₂×C₅×C₇×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₇	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₅×C₇×C₁₅₇

32 conjugacy classes of subgroups.

μ_t(G) = 16485

16485 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 13);