C₂×C₃⋊(C₂₉⋊((C₅⋊D₅)⋊C₃)) #39908076

order	26100
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₃⋊(C₂₉⋊((C₅⋊D₅)⋊C₃))
unambiguous semidirect product	(C₂×C₃)⋊(C₂₉⋊((C₅⋊D₅)⋊C₃))
unambiguous semidirect product	(C₂×C₂₉)⋊(C₃⋊((C₅⋊D₅)⋊C₃))
unambiguous semidirect product	(C₂×C₃⋊(C₅⋊D₁₄₅))⋊C₃

	subgroup	G/H
center, hypercenter	C₂	C₃⋊(C₂₉⋊((C₅⋊D₅)⋊C₃))
commutator, cosocle, hypocenter	C₃×C₅²×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₅²×C₂₉	C₂×C₃
LCS	G ▷ C₃×C₅²×C₂₉
UCS	C₁ ◁ C₂

128 conjugacy classes of subgroups.

μ_t(G) = 2610

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 310);