Finite Group Databasebeta

← Prev (#22579572) Next (#22579574) →

C₃×D₃×C₄₉₁ #22579573

order	8838
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄₉₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×D₃×C₄₉₁
unambiguous semidirect product	C₃⋊(C₂×C₃×C₄₉₁)

Splittings

Fitting, socle, Hall	C₃²×C₄₉₁ ⋊ C₂
derived	C₃ ⋊ C₂×C₃×C₄₉₁
Sylow	C₃² ⋊ C₂×C₄₉₁

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₉₁	D₃
commutator, hypocenter	C₃	C₂×C₃×C₄₉₁
Frattini	C₁	G
Fitting, socle	C₃²×C₄₉₁	C₂
LCS	G ▷ C₃
UCS	C₁ ◁ C₃×C₄₉₁

18 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4419 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×D₃×D₄₉₁, D₃²×C₄₉₁, D₃×D₁₄₇₃, …
maximal normal subgroup of	C₃×D₃×D₄₉₁, D₃²×C₄₉₁, D₃×D₁₄₇₃, …
maximal quotient of	C₃×Dic₃×C₄₉₁, C₂×C₃×D₃×C₄₉₁

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8838, 7);