D₃×D₂₃ #63283

order	276
isoclinism	isoclinic class of D₃×D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

direct product	D₃×D₂₃
unambiguous semidirect product	(D₃×C₂₃)⋊C₂
unambiguous semidirect product	(C₃×D₂₃)⋊C₂
unambiguous semidirect product	D₆₉⋊C₂

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

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 69

A minimal faithful permutation representation — 2 generators on 26 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(276, 5);