C₇×C₁₃×C₃⋊(D₁₉⋊C₃) #44527906

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₃×C₃⋊(D₁₉⋊C₃)
unambiguous semidirect product	C₃⋊(C₇×C₁₃×D₁₉⋊C₃)
unambiguous semidirect product	(C₁₉⋊C₃)⋊(D₃×C₇×C₁₃)
unambiguous semidirect product	D₅₇⋊(C₃×C₇×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₃⋊(D₁₉⋊C₃)
commutator, cosocle, hypocenter	C₃×C₁₉	C₂×C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₇×C₁₃

72 conjugacy classes of subgroups.

μ_t(G) = 5187

1638 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 389);