C₂×C₁₃×C₃₄₉⋊C₃ #41030366

order	27222
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₁₃×C₃₄₉⋊C₃
unambiguous semidirect product	(C₂×C₃₄₉)⋊(C₃×C₁₃)

	subgroup	G/H
center, hypercenter	C₂×C₁₃	C₃₄₉⋊C₃
commutator, cosocle, hypocenter	C₃₄₉	C₂×C₃×C₁₃
Frattini	C₁	G
Fitting, socle	C₂×C₁₃×C₃₄₉	C₃
LCS	G ▷ C₃₄₉
UCS	C₁ ◁ C₂×C₁₃

16 conjugacy classes of subgroups.

μ_t(G) = 9074

3094 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27222, 2);