C₂×C₉×C₂₇⋊C₃ #13090166

order	1458
nilpotency class	2
isoclinism	isoclinic class of H(3,𝔽₃)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₉² · Schur multiplier (H₂) = C₃×C₉

Aliases

direct product

C₂×C₉×C₂₇⋊C₃

Subgroups

	subgroup	G/H
center	C₂×C₉²	C₃²
commutator	C₃	C₂×C₃×C₉²
Frattini, cosocle	C₃×C₉	C₂×C₃³
socle	C₂×C₃²	C₃²×C₉
prime radical	C₂×C₃³	C₃×C₉
LCS	G ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₂×C₉² ◁ G

320 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 38
transitive degree	μ_t(G) = 486

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

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₉×#6875, C₂×C₉×D₂₇⋊C₃
maximal normal subgroup of	C₂×C₉×#6875, C₂×C₉×D₂₇⋊C₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1458, 240);

C2×C9×C27⋊C3 #13090166