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C₉×C₁₃×D₇×C₁₉ #44527535

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₃×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₉×C₁₃×D₇×C₁₉

Splittings

Subgroups

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

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15561

Conjugacy classes & character table

11115 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 18);