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D₇⋊C₉×C₁₉₁ #37562675

order	24066
automorphism	?
homology	Abelianization (H₁) = C₂×C₉×C₁₉₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₇⋊C₉×C₁₉₁
unambiguous semidirect product	D₇⋊(C₉×C₁₉₁)
unambiguous semidirect product	(C₇⋊C₉)⋊(C₂×C₁₉₁)
unambiguous semidirect product	(D₇×C₁₉₁)⋊C₉

Splittings

derived, Sylow	C₇ ⋊ C₂×C₉×C₁₉₁
Hall	C₇⋊C₉×C₁₉₁ ⋊ C₂
Hall	D₇×C₁₉₁ ⋊ C₉
Hall	C₇×C₁₉₁ ⋊ C₂×C₉
Hall	C₇⋊C₉ ⋊ C₂×C₁₉₁
Hall	D₇ ⋊ C₉×C₁₉₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉₁	AGL(1,𝔽₇)
commutator, hypocenter	C₇	C₂×C₉×C₁₉₁
Frattini	C₃	AGL(1,𝔽₇)×C₁₉₁
Fitting, socle	C₃×C₇×C₁₉₁	C₂×C₃
prime radical	C₃×D₇×C₁₉₁	C₃
cosocle	C₃×C₇	C₂×C₃×C₁₉₁
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₁₉₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 12033

Conjugacy classes & character table

4011 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24066, 11);