C₃×C₅×C₇×D₅×C₂₉ #44478603

order	30450
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₅×C₇×C₂₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×C₅×C₇×D₅×C₂₉
unambiguous semidirect product	C₅⋊(C₂×C₃×C₅×C₇×C₂₉)

	subgroup	G/H
center, hypercenter	C₃×C₅×C₇×C₂₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₃×C₅×C₇×C₂₉
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₇×C₂₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₃×C₅×C₇×C₂₉

80 conjugacy classes of subgroups.

μ_t(G) = 6090

12180 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 87);