D₅×C₃₁₃₇ #44535859

order	31370
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₁₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₃₁₃₇
unambiguous semidirect product	C₅⋊(C₂×C₃₁₃₇)

Fitting, socle, Hall	C₅×C₃₁₃₇ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₃₁₃₇

	subgroup	G/H
center, hypercenter	C₃₁₃₇	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃₁₃₇
Frattini	C₁	G
Fitting, socle	C₅×C₃₁₃₇	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃₁₃₇

8 conjugacy classes of subgroups.

μ_t(G) = 15685

12548 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31370, 1);