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C₁₃×C₁₇×C₇⋊C₉ #28358192

order	13923
isoclinism	isoclinic class of ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₁₇ · Schur multiplier (H₂) = C₁

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₁₇	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₉×C₁₃×C₁₇
Frattini	C₃	C₁₃×C₁₇×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₃×C₇×C₁₃×C₁₇	C₃
cosocle	C₃×C₇	C₃×C₁₃×C₁₇
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₃×C₁₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 13923

Conjugacy classes & character table

3315 conjugacy classes. The character table is too large to display.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13923, 3);