C₂×D₃×C₇×C₁₇×C₁₉ #41029624

order	27132
automorphism	?
homology	Abelianization (H₁) = C₂²×C₇×C₁₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₃×C₇×C₁₇×C₁₉
unambiguous semidirect product	C₃⋊(C₂²×C₇×C₁₇×C₁₉)
unambiguous semidirect product	(C₂×C₃)⋊(C₂×C₇×C₁₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₂×C₇×C₁₇×C₁₉	D₃
commutator, cosocle, hypocenter	C₃	C₂²×C₇×C₁₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₃×C₇×C₁₇×C₁₉	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₇×C₁₇×C₁₉

80 conjugacy classes of subgroups.

μ_t(G) = 13566

13566 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27132, 181);