A₄×D₁₉ #90725

order	456
isoclinism	isoclinic class of A₄×D₁₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

A₄×D₁₉

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₂²×C₁₉	C₂×C₃
LCS	G ▷ C₂²×C₁₉
UCS	C₁

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 23
transitive degree	μ_t(G) = 76

A minimal faithful permutation representation — 2 generators on 23 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 45);