C₄×#6887 #11757652

order	972
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₉ · Schur multiplier (H₂) = C₃×C₉

Aliases

direct product

C₄×#6887

Subgroups

	subgroup	G/H
center	C₃×C₄×C₉	C₃²
commutator	C₃	C₃²×C₄×C₉
Frattini, socle, cosocle	C₂×C₃²	C₂×C₃³
prime radical	C₂×C₃³	C₂×C₃²
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₄×C₉ ◁ G

207 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 40
transitive degree	μ_t(G) = 324

A minimal faithful permutation representation — 3 generators on 40 points:

(1,2,3,4)(5,6,8,7,9,11,10,12,13)(14,15,18)(16,20,26)(17,21,25)(19,27,24)(22,29,34)(23,30,33)(28,35,32)(31,37,39)(36,40,38);(15,19,21)(18,25,27)(20,28,30)(26,33,35)(29,36,37)(34,39,40);(14,16,22,17,23,31,24,32,38)(15,20,29,21,30,37,19,28,36)(18,26,34,25,33,39,27,35,40)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	#14516327, #14516328, #14516329, …
maximal subgroup of	#14516327, #14516328, #14516329, …
maximal normal subgroup of	#14516327, #14516328, #14516329, …
maximal quotient of	C₈×#6887, C₂×C₄×#6887

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(972, 377);

C4×#6887 #11757652