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C₇×C₁₇×C₁₃⋊C₉ #28358191

order	13923
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₇×C₉×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₇×C₁₃⋊C₉
unambiguous semidirect product	C₁₃⋊(C₇×C₉×C₁₇)
unambiguous semidirect product	(C₁₃×C₁₇)⋊(C₇×C₉)

Splittings

derived, Sylow	C₁₃ ⋊ C₇×C₉×C₁₇
Hall	C₇×C₁₃×C₁₇ ⋊ C₉
Hall	C₁₃×C₁₇ ⋊ C₇×C₉
Hall	C₇×C₁₃ ⋊ C₉×C₁₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₇×C₁₇	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₇×C₉×C₁₇
Frattini	C₃	C₇×C₁₇×C₁₃⋊C₃
Fitting, socle, prime radical	C₃×C₇×C₁₃×C₁₇	C₃
cosocle	C₃×C₁₃	C₃×C₇×C₁₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₃×C₇×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13923

Conjugacy classes & character table

2499 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₇×C₁₇×C₁₃⋊C₉, C₇×D₁₇×C₁₃⋊C₉, C₇×C₁₇×D₁₃⋊C₉, …
maximal normal subgroup of	C₂×C₇×C₁₇×C₁₃⋊C₉, C₇×D₁₇×C₁₃⋊C₉, C₇×C₁₇×D₁₃⋊C₉, …
maximal quotient of	C₂×C₇×C₁₇×C₁₃⋊C₉

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13923, 2);