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C₁₃×D₁₉×C₇⋊C₉ #44527551

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

Aliases

C₁₃×D₁₉×C₇⋊C₉

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	ΓL(1,𝔽₈)×D₁₉
commutator, hypocenter	C₇×C₁₉	C₂×C₉×C₁₃
Frattini	C₃	C₁₃×ΓL(1,𝔽₈)×D₁₉
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₇×C₁₃×D₁₉	C₃
cosocle	C₃×C₇×C₁₉	C₂×C₃×C₁₃
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₃×C₁₃

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15561

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 34);