C₃×C₇×C₁₉×D₁₃⋊C₃ #44527816

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃²×C₇×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃×C₇×C₁₉×D₁₃⋊C₃
unambiguous semidirect product	D₁₃⋊(C₃²×C₇×C₁₉)
unambiguous semidirect product	(C₁₃⋊C₃)⋊(C₂×C₃×C₇×C₁₉)
unambiguous semidirect product	(C₃×D₁₃)⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₉	D₁₃⋊C₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₃²×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₁₉

96 conjugacy classes of subgroups.

μ_t(G) = 5187

3192 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 299);