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C₃×C₂²⋊(C₁₉₃⋊C₃) #20294308

order	6948
automorphism	?
homology	Abelianization (H₁) = C₃² · Schur multiplier (H₂) = C₂×C₃

Aliases

direct product	C₃×C₂²⋊(C₁₉₃⋊C₃)
unambiguous semidirect product	(C₂²×C₃)⋊(C₁₉₃⋊C₃)
unambiguous semidirect product	(C₃×C₁₉₃)⋊A₄

Splittings

Fitting, socle	C₂²×C₃×C₁₉₃ ⋊ C₃
derived, Hall	C₂²×C₁₉₃ ⋊ C₃²
Sylow	C₁₉₃ ⋊ C₃×A₄
Sylow	C₂² ⋊ C₃×C₁₉₃⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₂²⋊(C₁₉₃⋊C₃)
commutator, hypocenter	C₂²×C₁₉₃	C₃²
Frattini	C₁	G
Fitting, socle	C₂²×C₃×C₁₉₃	C₃
LCS	G ▷ C₂²×C₁₉₃
UCS	C₁ ◁ C₃

28 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

780 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₃×C₅×C₂²⋊(C₁₉₃⋊C₃)
maximal normal subgroup of	C₃×C₅×C₂²⋊(C₁₉₃⋊C₃)
maximal quotient of	C₃×C₅×C₂²⋊(C₁₉₃⋊C₃)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6948, 48);