C₅×D₂₁×C₁₅₇ #45682131

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

Aliases

direct product	C₅×D₂₁×C₁₅₇
unambiguous semidirect product	C₃⋊(C₅×D₇×C₁₅₇)
unambiguous semidirect product	C₇⋊(C₅×D₃×C₁₅₇)

	subgroup	G/H
center, hypercenter	C₅×C₁₅₇	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₅×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₇	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₅₇

32 conjugacy classes of subgroups.

μ_t(G) = 16485

9420 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 15);