Finite Group Databasebeta

← Prev (#44535626) Next (#44535628) →

C₆₇×C₂²⋊(C₁₃⋊C₉) #44535627

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

Aliases

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

Splittings

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

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 15678

Conjugacy classes & character table

4020 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 63);