C₅×D₂₁×C₁₅₁ #44540251

order	31710
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₁₅₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₂₁×C₁₅₁
unambiguous semidirect product	C₃⋊(C₅×D₇×C₁₅₁)
unambiguous semidirect product	C₇⋊(C₅×D₃×C₁₅₁)

	subgroup	G/H
center, hypercenter	C₅×C₁₅₁	D₂₁
commutator, cosocle, hypocenter	C₃×C₇	C₂×C₅×C₁₅₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₇
UCS	C₁ ◁ C₅×C₁₅₁

32 conjugacy classes of subgroups.

μ_t(G) = 15855

9060 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 20);