C₇×D₁₅×C₁₅₇ #45682133

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

Aliases

direct product	C₇×D₁₅×C₁₅₇
unambiguous semidirect product	C₃⋊(C₇×D₅×C₁₅₇)
unambiguous semidirect product	C₅⋊(D₃×C₇×C₁₅₇)

	subgroup	G/H
center, hypercenter	C₇×C₁₅₇	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₇×C₁₅₇
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₇	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₅₇

32 conjugacy classes of subgroups.

μ_t(G) = 16485

9891 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32970, 17);