D₃₃⋊C₄ #63139

order	264
isoclinism	isoclinic class of D₃×D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

D₃₃⋊C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₁
commutator, hypocenter	C₃×C₁₁	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₁	C₂²
prime radical	C₂×D₃₃	C₂
LCS	G ▷ C₃×C₁₁
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 18
transitive degree	μ_t(G) = 132

A minimal faithful permutation representation — 2 generators on 18 points:

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

Polycyclic presentation:

2^3,3,11|a^2=c,b^2=c,e^a=e^10,d^b=d^2

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(264, 7);