C₅×D₃₁₃₇ #44535860

order	31370
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅×D₃₁₃₇
unambiguous semidirect product	C₃₁₃₇⋊(C₂×C₅)

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

	subgroup	G/H
center, hypercenter	C₅	D₃₁₃₇
commutator, cosocle, hypocenter	C₃₁₃₇	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₅×C₃₁₃₇	C₂
LCS	G ▷ C₃₁₃₇
UCS	C₁ ◁ C₅

8 conjugacy classes of subgroups.

μ_t(G) = 15685

7850 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31370, 2);