Finite Group Databasebeta

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C₁₉×(C₁₃⋊C₉)⋊D₇ #44527613

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

Aliases

direct product	C₁₉×(C₁₃⋊C₉)⋊D₇
unambiguous semidirect product	(C₁₃⋊C₉)⋊(D₇×C₁₉)

Splittings

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	(C₁₃⋊C₃)⋊D₇
commutator, hypocenter	C₇×C₁₃	C₂×C₉×C₁₉
Frattini	C₃	C₁₉×(C₁₃⋊C₃)⋊D₇
Fitting, socle	C₃×C₇×C₁₃×C₁₉	C₂×C₃
prime radical	C₃×C₁₉×D₉₁	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

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31122, 96);