Finite Group Databasebeta

← Prev (#46800794) Next (#46800796) →

Dic₃×C₁₉×C₁₄₉ #46800795

order	33972
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₁₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉×C₁₄₉
unambiguous semidirect product	C₃⋊(C₄×C₁₉×C₁₄₉)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₉×C₁₄₉
Hall	C₃×C₁₉×C₁₄₉ ⋊ C₄
Hall	C₃×C₁₄₉ ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄×C₁₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₄₉	D₃
commutator, hypocenter	C₃	C₄×C₁₉×C₁₄₉
Frattini	C₂	D₃×C₁₉×C₁₄₉
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₁₄₉	C₂
cosocle	C₂×C₃	C₂×C₁₉×C₁₄₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₄₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33972

Conjugacy classes & character table

16986 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33972, 6);