Finite Group Databasebeta

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C₂×C₇×C₁₉×C₁₃⋊C₉ #44527520

order	31122
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂×C₇×C₁₉×C₁₃⋊C₉
unambiguous semidirect product	(C₂×C₁₃)⋊(C₇×C₉×C₁₉)

Splittings

Subgroups

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

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 31122

Conjugacy classes & character table

5586 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 3);