C₁₃×D₂₅×C₁₉⋊C₃ #49150207

order	37050
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₂₅×C₁₉⋊C₃
unambiguous semidirect product	C₂₅⋊(C₂×C₁₃×C₁₉⋊C₃)
unambiguous semidirect product	(C₁₉×D₂₅)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₁₃	D₂₅×C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉×C₂₅	C₂×C₃×C₁₃
Frattini	C₅	D₅×C₁₃×C₁₉⋊C₃
Fitting	C₁₃×C₁₉×C₂₅	C₂×C₃
socle	C₅×C₁₃×C₁₉	C₃×D₅
LCS	G ▷ C₁₉×C₂₅
UCS	C₁ ◁ C₁₃

48 conjugacy classes of subgroups.

μ_t(G) = 6175

1638 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37050, 33);