C₂×C₃×C₁₉×C₉₇⋊C₃ #45684346

order	33174
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₂×C₃×C₁₉×C₉₇⋊C₃
unambiguous semidirect product	(C₂×C₉₇)⋊(C₃²×C₁₉)
unambiguous semidirect product	(C₂×C₃×C₉₇)⋊(C₃×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₉₇⋊C₃
commutator, cosocle, hypocenter	C₉₇	C₂×C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₁₉×C₉₇	C₃
LCS	G ▷ C₉₇
UCS	C₁ ◁ C₂×C₃×C₁₉

48 conjugacy classes of subgroups.

μ_t(G) = 11058

3990 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33174, 70);