C₁₃×C₃⋊(C₅⋊(C₇⋊D₇)) #34062186

order	19110
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₁₃×C₃⋊(C₅⋊(C₇⋊D₇))
unambiguous semidirect product	C₃⋊(C₁₃×C₅⋊(C₇⋊D₇))
unambiguous semidirect product	C₅⋊(C₁₃×C₃⋊(C₇⋊D₇))
unambiguous semidirect product	C₇⋊(C₁₃×D₁₀₅)

	subgroup	G/H
center, hypercenter	C₁₃	C₃⋊(C₅⋊(C₇⋊D₇))
commutator, cosocle, hypocenter	C₃×C₅×C₇²	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₅×C₇²×C₁₃	C₂
LCS	G ▷ C₃×C₅×C₇²
UCS	C₁ ◁ C₁₃

160 conjugacy classes of subgroups.

μ_t(G) = 9555

4797 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 179);