#92285

order	486
automorphism	?
homology	Abelianization (H₁) = C₂×C₃² · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

Splittings

Fitting, Sylow

#6911 ⋊ C₂

Subgroups

	subgroup	G/H
center, socle	C₃	C₃×(C₃⋊D₃)⋊C₃
commutator, cosocle, hypocenter	H(3,𝔽₃)	C₂×C₃²
Frattini	C₃²	C₃²×D₃
Fitting	#6911	C₂
hypercenter	C₃²	(C₃⋊D₃)⋊C₃
LCS	G ▷ H(3,𝔽₃)
UCS	C₁ ◁ C₃ ◁ C₃²

82 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 27

A minimal faithful permutation representation — 2 generators on 27 points:

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

Polycyclic presentation:

2,3^5|b^3=f,d^a=d^2,e^a=e^2f,c^b=cf,d^b=de,e^d=ef

Conjugacy classes & character table

34 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	(#4178⋊C₂)⋊C₃, C₂×#92285, #13091106, …
maximal normal subgroup of	(#4178⋊C₂)⋊C₃, C₂×#92285, #13091106, …
maximal quotient of	#11757589, C₂×#92285, #13090732, …
automorphism group of	#733, C₂×#733

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 130);