C₂×C₅²×C₃⋊D₃×C₃₇ #45686520

order	33300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅²×C₃₇ · Schur multiplier (H₂) = C₂×C₃×C₅

Aliases

direct product	C₂×C₅²×C₃⋊D₃×C₃₇
unambiguous semidirect product	(C₂×C₃)⋊(C₅²×D₃×C₃₇)

	subgroup	G/H
center, hypercenter	C₂×C₅²×C₃₇	C₃⋊D₃
commutator, cosocle, hypocenter	C₃²	C₂²×C₅²×C₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₃²×C₅²×C₃₇	C₂
LCS	G ▷ C₃²
UCS	C₁ ◁ C₂×C₅²×C₃₇

480 conjugacy classes of subgroups.

μ_t(G) = 16650

11100 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 793);