Finite Group Databasebeta

← Prev (#72244097) Next (#72244099) →

C₂×#13091525 #72244098

order	2916
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃³ · Schur multiplier (H₂) = C₂×C₃²

Aliases

C₂×#13091525

Splittings

Fitting	C₂×#10624900 ⋊ C₂
Sylow	#10624900 ⋊ C₂²

Subgroups

	subgroup	G/H
center	C₂×C₃	C₃²×AGL(1,ℤ/9)
commutator, cosocle	C₃×C₉	C₂²×C₃³
Frattini	C₃²	C₂×C₃³×D₃
Fitting	C₂×#10624900	C₂
socle	C₂×C₃²	C₃³×D₃
prime radical	C₂×D₉×H(3,𝔽₃)	C₃
hypercenter	C₂×H(3,𝔽₃)	AGL(1,ℤ/9)
hypocenter	C₉	C₂²×#737
LCS	G ▷ C₃×C₉ ▷ C₉
UCS	C₁ ◁ C₂×C₃ ◁ C₂×H(3,𝔽₃)

761 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 108

Conjugacy classes & character table

220 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×#72221845, C₂×#72221864
maximal normal subgroup of	C₂×#72221864
maximal quotient of	C₂×#72221846

GAP

Past the SmallGroups library coverage — no SmallGroups id.