C₅²×D₃×C₂₉⋊C₇ #44478562

order	30450
automorphism	?
homology	Abelianization (H₁) = C₂×C₅²×C₇ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²×D₃×C₂₉⋊C₇
unambiguous semidirect product	C₃⋊(C₂×C₅²×C₂₉⋊C₇)
unambiguous semidirect product	(D₃×C₂₉)⋊(C₅²×C₇)
unambiguous semidirect product	(C₅×D₃×C₂₉)⋊(C₅×C₇)
unambiguous semidirect product	(C₅²×D₃×C₂₉)⋊C₇

	subgroup	G/H
center, hypercenter	C₅²	D₃×C₂₉⋊C₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₅²×C₇
Frattini	C₁	G
Fitting, socle	C₃×C₅²×C₂₉	C₂×C₇
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₅²

128 conjugacy classes of subgroups.

μ_t(G) = 2175

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30450, 46);