Finite Group Databasebeta

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C₁₃×C₂²⋊C₉×C₆₇ #44535629

order	31356
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₃×C₆₇ · Schur multiplier (H₂) = C₂

Aliases

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

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₃×C₆₇	A₄
commutator, hypocenter	C₂²	C₉×C₁₃×C₆₇
Frattini	C₃	A₄×C₁₃×C₆₇
Fitting, socle, prime radical	C₂²×C₃×C₁₃×C₆₇	C₃
cosocle	C₂²×C₃	C₃×C₁₃×C₆₇
LCS	G ▷ C₂²
UCS	C₁ ◁ C₃×C₁₃×C₆₇

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15678

Conjugacy classes & character table

10452 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 65);