C₂×C₅⋊(C₂₉⋊(D₁₃⋊C₃)) #36383135

order	22620
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅⋊(C₂₉⋊(D₁₃⋊C₃))
unambiguous semidirect product	(C₂×C₅)⋊(C₂₉⋊(D₁₃⋊C₃))
unambiguous semidirect product	(C₂×C₂₉)⋊(C₅⋊(D₁₃⋊C₃))
unambiguous semidirect product	(C₂×C₁₃⋊C₃)⋊D₁₄₅
unambiguous semidirect product	(C₂×D₁₈₈₅)⋊C₃

	subgroup	G/H
center, hypercenter	C₂	C₅⋊(C₂₉⋊(D₁₃⋊C₃))
commutator, cosocle, hypocenter	C₅×C₁₃×C₂₉	C₂²×C₃
Frattini	C₁	G
Fitting, socle	C₂×C₅×C₁₃×C₂₉	C₂×C₃
LCS	G ▷ C₅×C₁₃×C₂₉
UCS	C₁ ◁ C₂

80 conjugacy classes of subgroups.

μ_t(G) = 3770

1024 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22620, 65);