Dic₃×D₁₉ #90692

order	456
isoclinism	isoclinic class of D₃×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂

Aliases

direct product	Dic₃×D₁₉
unambiguous semidirect product	(C₃×D₁₉)⋊C₄

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×D₁₉
commutator, hypocenter	C₃×C₁₉	C₂×C₄
Fitting, socle, cosocle	C₂×C₃×C₁₉	C₂²
prime radical	C₂×C₃×D₁₉	C₂
LCS	G ▷ C₃×C₁₉
UCS	C₁ ◁ C₂

32 conjugacy classes of subgroups.

minimal degree	μ(G) = 26
transitive degree	μ_t(G) = 228

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 12);