C₂×C₁₉⋊C₃×D₁₁₅ #39910753

order	26220
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉⋊C₃×D₁₁₅
unambiguous semidirect product	(C₂×C₅)⋊(D₂₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₂₃)⋊(D₅×C₁₉⋊C₃)
unambiguous semidirect product	(C₂×C₁₉×D₁₁₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₂	C₁₉⋊C₃×D₁₁₅
commutator, cosocle, hypocenter	C₅×C₁₉×C₂₃	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₉×C₂₃	C₂×C₃
LCS	G ▷ C₅×C₁₉×C₂₃
UCS	C₁ ◁ C₂

80 conjugacy classes of subgroups.

μ_t(G) = 4370

1062 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26220, 43);