C₂×C₇×C₂₉×C₅²⋊C₃ #44478597

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

Aliases

direct product	C₂×C₇×C₂₉×C₅²⋊C₃
unambiguous semidirect product	(C₂×C₅²)⋊(C₃×C₇×C₂₉)

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

48 conjugacy classes of subgroups.

μ_t(G) = 6090

4466 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 81);