Finite Group Databasebeta

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C₃×#10707070 #72222603

order	2304
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃×C₈ · Schur multiplier (H₂) = C₂³

Aliases

C₃×#10707070

Splittings

Fitting	C₃²×#1580 ⋊ C₂
Sylow	C₃² ⋊ #12067

Subgroups

	subgroup	G/H
center	C₂²×C₃	#5014
commutator	C₃×C₈	C₂²×C₃×C₈
Frattini	C₄×C₈	C₂²×C₃×D₃
Fitting	C₃²×#1580	C₂
socle	C₂²×C₃²	#442
prime radical	C₂×C₃×#826	C₄
cosocle	C₃×C₄×C₈	C₂³×C₃
hypercenter	C₃×#1580	D₃
hypocenter	C₃	C₃×#12067
LCS	G ▷ C₃×C₈ ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#322 ◁ C₃×#1580

588 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#72222659
maximal normal subgroup of	#72222659
maximal quotient of	C₃×#72222516

GAP

Past the SmallGroups library coverage — no SmallGroups id.