C₃×C₇×C₂₉×C₅⋊D₅ #44478607

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

Aliases

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

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

128 conjugacy classes of subgroups.

μ_t(G) = 15225

8526 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 91);