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C₇×D₁₉×C₁₃⋊C₉ #44527548

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

Aliases

C₇×D₁₉×C₁₃⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇	D₁₉×C₁₃⋊C₃
commutator, hypocenter	C₁₃×C₁₉	C₂×C₇×C₉
Frattini	C₃	C₇×D₁₉×C₁₃⋊C₃
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₇×C₁₃×D₁₉	C₃
cosocle	C₃×C₁₃×C₁₉	C₂×C₃×C₇
LCS	G ▷ C₁₃×C₁₉
UCS	C₁ ◁ C₃×C₇

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15561

Conjugacy classes & character table

1617 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 31);