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C₁₉×#13109901 #44527596

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×#13109901

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#10587721
commutator, hypocenter	C₇×C₁₃	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×#10587721
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₁₃×D₇×C₁₉	C₃
cosocle	C₃×C₇×C₁₃	C₂×C₃×C₁₉
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₃×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15561

Conjugacy classes & character table

1539 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 79);