C₉⋊#261 #90835

order	468
isoclinism	isoclinic class of C₉⋊#261
automorphism	?
homology	Abelianization (H₁) = C₄ · Schur multiplier (H₂) = C₁

Aliases

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, hypocenter	C₉×C₁₃	C₄
Frattini	C₃	C₃⋊#261
socle	C₃×C₁₃	Dic₃
prime radical	C₃×D₁₃	D₃
cosocle	C₉×D₁₃	C₂
LCS	G ▷ C₉×C₁₃
UCS	C₁

18 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 117

A minimal faithful permutation representation — 2 generators on 22 points:

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

Polycyclic presentation:

2^2,3,13,3|a^2=b,c^3=e^2,c^a=c^2e,d^a=d^5,e^a=e^2,d^b=d^12

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(468, 10);