C₃²×#2171 #11769220

order	1152
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃²×C₈ · Schur multiplier (H₂) = C₂²×C₃

Aliases

direct product

C₃²×#2171

Subgroups

	subgroup	G/H
center	C₃²×C₈	C₂×D₄
commutator	C₄	C₂²×C₃²×C₈
Frattini, cosocle	C₂×C₈	C₂³×C₃²
socle	C₂×C₃²	C₈×D₄
prime radical	C₃²×#135	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₃²×C₈ ◁ C₂×C₃²×C₁₆ ◁ G

432 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 288

A minimal faithful permutation representation — 3 generators on 38 points:

(1,2,3)(7,8,12,18,13,17,30,36,14,19,31,21,11,27,29,37)(9,20,23,25,22,15,32,26,16,33,35,24,28,34,38,10);(4,5,6)(7,9)(8,15)(10,21)(11,28)(12,23)(13,22)(14,16)(17,33)(18,26)(19,34)(20,27)(24,36)(25,37)(29,38)(30,32)(31,35);(7,10,12,20,13,25,30,15,14,26,31,33,11,24,29,34)(8,16,18,35,17,28,36,38,19,9,21,23,27,22,37,32)

Conjugacy classes & character table

396 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	C₃⋊D₃×#2171, #72255425
maximal subgroup of	C₃²×#12068, C₃⋊D₃×#2171, #72255425
maximal normal subgroup of	C₃²×#12068, C₃⋊D₃×#2171, #72255425
maximal quotient of	C₃²×#12062

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 3231);

C32×#2171 #11769220

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃²×#2171 #11769220