Finite Group Databasebeta

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C₂×D₉×C₁₉₃ #20294277

order	6948
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×D₉×C₁₉₃
unambiguous semidirect product	C₉⋊(C₂²×C₁₉₃)
unambiguous semidirect product	(C₂×C₉)⋊(C₂×C₁₉₃)

Splittings

Fitting	C₂×C₉×C₁₉₃ ⋊ C₂
derived, Sylow	C₉ ⋊ C₂²×C₁₉₃
Hall	C₉×C₁₉₃ ⋊ C₂²

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉₃	D₉
commutator, hypocenter	C₉	C₂²×C₁₉₃
Frattini	C₃	C₂×D₃×C₁₉₃
Fitting	C₂×C₉×C₁₉₃	C₂
socle	C₂×C₃×C₁₉₃	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉₃

30 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2316 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₅×D₉×C₁₉₃, C₂×D₄₅×C₁₉₃, C₂×C₅×D₉×C₁₉₃
maximal normal subgroup of	C₂×C₅×D₉×C₁₉₃
maximal quotient of	D₅×D₉×C₁₉₃, C₂×D₄₅×C₁₉₃, C₂×C₅×D₉×C₁₉₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6948, 17);