C₂³×#6875 #14516713

order	1944
nilpotency class	3
isoclinism	isoclinic class of #6875
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃×C₉ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂³×#6875

Subgroups

	subgroup	G/H
center, socle	C₂³×C₃	C₉⋊C₉
commutator	C₉	C₂³×C₃×C₉
Frattini, cosocle	C₃×C₉	C₂³×C₃²
prime radical	C₂³×C₃²	3₋¹⁺²
LCS	G ▷ C₉ ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₂³×C₃×C₉ ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 216

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₂×A₄×#6875, C₂³×AGL(1,ℤ/27), C₂×#14516071
maximal subgroup of	C₂×A₄×#6875, C₂³×#11757417, C₂×D₄×#6875, …
maximal normal subgroup of	C₂×A₄×#6875, C₂×D₄×#6875, C₂³×AGL(1,ℤ/27), …
maximal quotient of	C₂³×#11757417, C₂×D₄×#6875

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1944, 1107);

C23×#6875 #14516713