Finite Group Databasebeta

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C₂×C₉×C₁₃×D₆₇ #44535640

order	31356
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₁₃×D₆₇

Splittings

Fitting	C₂×C₉×C₁₃×C₆₇ ⋊ C₂
derived, Sylow	C₆₇ ⋊ C₂²×C₉×C₁₃
Hall	C₉×C₁₃×C₆₇ ⋊ C₂²
Hall	C₁₃×C₆₇ ⋊ C₂²×C₉
Hall	C₉×C₆₇ ⋊ C₂²×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₃	D₆₇
commutator, hypocenter	C₆₇	C₂²×C₉×C₁₃
Frattini	C₃	C₂×C₃×C₁₃×D₆₇
Fitting	C₂×C₉×C₁₃×C₆₇	C₂
socle	C₂×C₃×C₁₃×C₆₇	C₂×C₃
prime radical	C₂×C₃×C₁₃×D₆₇	C₃
cosocle	C₃×C₆₇	C₂²×C₃×C₁₃
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₉×C₁₃

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15678

Conjugacy classes & character table

8190 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 76);