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C₁₃⋊C₉×C₁₃₇ #30630955

order	16029
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₉×C₁₃₇
unambiguous semidirect product	C₁₃⋊(C₉×C₁₃₇)
unambiguous semidirect product	(C₁₃×C₁₃₇)⋊C₉

Splittings

derived, Sylow	C₁₃ ⋊ C₉×C₁₃₇
Hall	C₁₃×C₁₃₇ ⋊ C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃₇	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₉×C₁₃₇
Frattini	C₃	C₁₃⋊C₃×C₁₃₇
Fitting, socle, prime radical	C₃×C₁₃×C₁₃₇	C₃
cosocle	C₃×C₁₃	C₃×C₁₃₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₁₃₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16029

Conjugacy classes & character table

2877 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₃⋊C₉×C₁₃₇, C₁₃⋊C₉×D₁₃₇, C₁₃₇×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₁₃⋊C₉×C₁₃₇, C₁₃⋊C₉×D₁₃₇, C₁₃₇×D₁₃⋊C₉, …
maximal quotient of	C₂×C₁₃⋊C₉×C₁₃₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16029, 2);