C₂²×C₃²×#123 #11770483

order	1152
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₃² · Schur multiplier (H₂) = C₂⁹×C₃

Aliases

C₂²×C₃²×#123

	subgroup	G/H
center, socle	C₂⁴×C₃²	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃²
prime radical	C₂³×C₃²×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₃² ◁ G

5904 conjugacy classes of subgroups.

minimal degree	μ(G) = 22
transitive degree	μ_t(G) = 576

A minimal faithful permutation representation — 5 generators on 22 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 4494);