Finite Group Databasebeta

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C₂×#72222571 #72255386

order	4608
automorphism	?
homology	Abelianization (H₁) = C₂³×C₈ · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₂×#72222571

Splittings

Fitting	C₂×C₃²×#1333 ⋊ C₂
Sylow	C₃² ⋊ C₂×#12067

Subgroups

	subgroup	G/H
center	C₂³	#10592484
commutator	C₃²×C₈	C₂³×C₈
Frattini	C₄×C₈	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#1333	C₂
socle	C₂³×C₃²	#442
prime radical	C₂²×#63653	C₄
cosocle	C₃²×C₄×C₈	C₂⁴
hypercenter	C₂×#1333	C₃⋊D₃
hypocenter	C₃²	C₂×#12067
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×#1333

3468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2304

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₃⋊D₃×#12067
maximal normal subgroup of	C₂×C₃⋊D₃×#12067

GAP

Past the SmallGroups library coverage — no SmallGroups id.