C₇×D₁₅×C₁₅₁ #44540253

order	31710
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₅₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₅×C₁₅₁
unambiguous semidirect product	C₃⋊(C₇×D₅×C₁₅₁)
unambiguous semidirect product	C₅⋊(D₃×C₇×C₁₅₁)

	subgroup	G/H
center, hypercenter	C₇×C₁₅₁	D₁₅
commutator, cosocle, hypocenter	C₃×C₅	C₂×C₇×C₁₅₁
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇×C₁₅₁	C₂
LCS	G ▷ C₃×C₅
UCS	C₁ ◁ C₇×C₁₅₁

32 conjugacy classes of subgroups.

μ_t(G) = 15855

9513 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31710, 22);