Finite Group Databasebeta

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C₁₃×C₂²⋊(C₆₇⋊C₉) #44535628

order	31356
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₃×C₂²⋊(C₆₇⋊C₉)
unambiguous semidirect product	C₂²⋊(C₁₃×C₆₇⋊C₉)
unambiguous semidirect product	C₆₇⋊(C₁₃×C₂²⋊C₉)

Splittings

derived, Hall	C₂²×C₆₇ ⋊ C₉×C₁₃
Hall	C₂²×C₁₃×C₆₇ ⋊ C₉
Hall	C₁₃×C₆₇ ⋊ C₂²⋊C₉
Sylow	C₆₇ ⋊ C₁₃×C₂²⋊C₉
Hall	C₂²×C₁₃ ⋊ C₆₇⋊C₉
Sylow	C₂² ⋊ C₁₃×C₆₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃	C₂²⋊(C₆₇⋊C₃)
commutator, hypocenter	C₂²×C₆₇	C₉×C₁₃
Frattini	C₃	C₁₃×C₂²⋊(C₆₇⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₆₇	C₃
cosocle	C₂²×C₃×C₆₇	C₃×C₁₃
LCS	G ▷ C₂²×C₆₇
UCS	C₁ ◁ C₃×C₁₃

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15678

Conjugacy classes & character table

3588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 64);