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C₆₁×C₂²⋊(C₇⋊C₉) #29506757

order	15372
isoclinism	isoclinic class of C₂²⋊ΓL(1,𝔽₈)
automorphism	?
homology	Abelianization (H₁) = C₉×C₆₁ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₆₁×C₂²⋊(C₇⋊C₉)
unambiguous semidirect product	C₂²⋊(C₆₁×C₇⋊C₉)
unambiguous semidirect product	C₇⋊(C₂²⋊C₉×C₆₁)

Splittings

derived, Hall	C₂²×C₇ ⋊ C₉×C₆₁
Hall	C₂²×C₇×C₆₁ ⋊ C₉
Hall	C₇×C₆₁ ⋊ C₂²⋊C₉
Hall	C₂²×C₆₁ ⋊ C₇⋊C₉
Sylow	C₇ ⋊ C₂²⋊C₉×C₆₁
Sylow	C₂² ⋊ C₆₁×C₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₆₁	C₂²⋊ΓL(1,𝔽₈)
commutator, hypocenter	C₂²×C₇	C₉×C₆₁
Frattini	C₃	C₆₁×C₂²⋊ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂²×C₃×C₇×C₆₁	C₃
cosocle	C₂²×C₃×C₇	C₃×C₆₁
LCS	G ▷ C₂²×C₇
UCS	C₁ ◁ C₃×C₆₁

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 7686

Conjugacy classes & character table

2196 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15372, 67);