C₃₁×C₁₈₁⋊C₅ #43242582

order	28055
automorphism	?
homology	Abelianization (H₁) = C₅×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×C₁₈₁⋊C₅
unambiguous semidirect product	C₁₈₁⋊(C₅×C₃₁)

Fitting, socle, Hall	C₃₁×C₁₈₁ ⋊ C₅
derived, Sylow	C₁₈₁ ⋊ C₅×C₃₁

	subgroup	G/H
center, hypercenter	C₃₁	C₁₈₁⋊C₅
commutator, cosocle, hypocenter	C₁₈₁	C₅×C₃₁
Frattini	C₁	G
Fitting, socle	C₃₁×C₁₈₁	C₅
LCS	G ▷ C₁₈₁
UCS	C₁ ◁ C₃₁

8 conjugacy classes of subgroups.

μ_t(G) = 5611

1271 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28055, 2);