C₇×C₃⋊(C₃⋊(D₄₁⋊C₅)) #38788949

order	25830
automorphism	?
homology	Abelianization (H₁) = C₂×C₅×C₇ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₇×C₃⋊(C₃⋊(D₄₁⋊C₅))
unambiguous semidirect product	C₃⋊(C₇×C₃⋊(D₄₁⋊C₅))
unambiguous semidirect product	(C₄₁⋊C₅)⋊(C₇×C₃⋊D₃)
unambiguous semidirect product	(C₃⋊D₁₂₃)⋊(C₅×C₇)
unambiguous semidirect product	(C₇×C₃⋊D₁₂₃)⋊C₅

	subgroup	G/H
center, hypercenter	C₇	C₃⋊(C₃⋊(D₄₁⋊C₅))
commutator, cosocle, hypocenter	C₃²×C₄₁	C₂×C₅×C₇
Frattini	C₁	G
Fitting, socle	C₃²×C₇×C₄₁	C₂×C₅
LCS	G ▷ C₃²×C₄₁
UCS	C₁ ◁ C₇

96 conjugacy classes of subgroups.

μ_t(G) = 2583

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 53);