C₂×C₃×#6895 #13090357

order	1458
nilpotency class	2
isoclinism	isoclinic class of C₃²⋊H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃⁴ · Schur multiplier (H₂) = C₃⁵

Aliases

direct product

C₂×C₃×#6895

Subgroups

	subgroup	G/H
center, socle	C₂×C₃³	C₃³
commutator, Frattini, cosocle	C₃²	C₂×C₃⁴
prime radical	C₂×C₃⁴	C₃²
LCS	G ▷ C₃² ▷ C₁
UCS	C₁ ◁ C₂×C₃³ ◁ G

836 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 41
transitive degree	μ_t(G) = 486

A minimal faithful permutation representation — 4 generators on 41 points:

(1,2)(3,4,5);(6,7,9,8,11,13,12,10,14)(15,16,19)(17,21,27)(18,22,26)(20,28,25)(23,30,35)(24,31,34)(29,36,33)(32,38,40)(37,41,39);(16,20,22)(19,26,28)(21,29,31)(27,34,36)(30,37,38)(35,40,41);(7,10,11)(9,13,14)(15,17,23,18,24,32,25,33,39)(16,21,30,22,31,38,20,29,37)(19,27,35,26,34,40,28,36,41)

Conjugacy classes & character table

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

Relationships

Fitting subgroup of	C₂×C₃×#6895⋊C₂
maximal subgroup of	C₂×#14552273, C₂×C₃×#6895⋊C₂
maximal normal subgroup of	C₂×#14552273, C₂×C₃×#6895⋊C₂
maximal quotient of	C₂×#14554636

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 431);

C2×C3×#6895 #13090357