Finite Group Databasebeta

← Prev (#44535581) Next (#44535583) →

C₆₇×Dic₁₃⋊C₉ #44535582

order	31356
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₆₇×Dic₁₃⋊C₉
unambiguous semidirect product	Dic₁₃⋊(C₉×C₆₇)

Splittings

derived, Sylow	C₁₃ ⋊ C₄×C₉×C₆₇
Hall	C₆₇×C₁₃⋊C₉ ⋊ C₄
Hall	Dic₁₃×C₆₇ ⋊ C₉
Hall	C₁₃×C₆₇ ⋊ C₄×C₉
Hall	C₁₃⋊C₉ ⋊ C₄×C₆₇
Hall	Dic₁₃ ⋊ C₉×C₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₆₇	D₁₃⋊C₃
commutator, hypocenter	C₁₃	C₄×C₉×C₆₇
Frattini	C₂×C₃	C₆₇×D₁₃⋊C₃
Fitting, socle, prime radical	C₂×C₃×C₁₃×C₆₇	C₂×C₃
cosocle	C₂×C₃×C₁₃	C₂×C₃×C₆₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₂×C₃×C₆₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 31356

Conjugacy classes & character table

3216 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31356, 18);