#92197

order	486
isoclinism	isoclinic class of #92197
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₃

Aliases

No aliases for this group.

Splittings

Fitting, derived, Sylow

#6855 ⋊ C₂

Subgroups

	subgroup	G/H
center, hypercenter	C₃	C₉⋊D₉
commutator, Fitting, cosocle, hypocenter	#6855	C₂
Frattini, socle	C₃³	C₃⋊D₃
LCS	G ▷ #6855
UCS	C₁ ◁ C₃

102 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 27
transitive degree	μ_t(G) = 162

A minimal faithful permutation representation — 3 generators on 27 points:

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

Polycyclic presentation:

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

Conjugacy classes & character table

54 conjugacy classes — view the full character table.

Relationships

derived subgroup of	#11757369⋊C₂, #14516413
maximal subgroup of	#11757369, #92158⋊C₂, C₂×#92197, …
maximal normal subgroup of	#11757369, #92158⋊C₂, C₂×#92197, …
maximal quotient of	#11757320, C₂×#92197, #13090482, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(486, 42);