C₂×C₃₁₂₁⋊C₅ #44530116

order	31210
automorphism	?
homology	Abelianization (H₁) = C₂×C₅ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₃₁₂₁⋊C₅
unambiguous semidirect product	(C₂×C₃₁₂₁)⋊C₅

Fitting, socle, Hall	C₂×C₃₁₂₁ ⋊ C₅
derived, Sylow	C₃₁₂₁ ⋊ C₂×C₅

	subgroup	G/H
center, hypercenter	C₂	C₃₁₂₁⋊C₅
commutator, cosocle, hypocenter	C₃₁₂₁	C₂×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₃₁₂₁	C₅
LCS	G ▷ C₃₁₂₁
UCS	C₁ ◁ C₂

8 conjugacy classes of subgroups.

μ_t(G) = 6242

1258 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31210, 2);