D₃₃⋊D₂₃ #15690107

order	3036
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

unambiguous semidirect product	D₃₃⋊D₂₃
unambiguous semidirect product	D₆₉⋊D₁₁
unambiguous semidirect product	D₂₅₃⋊D₃

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₁×C₂₃	C₂²
LCS	G ▷ C₃×C₁₁×C₂₃
UCS	C₁

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 759

Polycyclic presentation:

2^2,3,11,23|d^a=d^10,e^a=e^22,c^b=c^2,d^b=d^10

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3036, 26);