C₂³×C₁₉⋊C₃ #90728

order	456
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂³×C₃ · Schur multiplier (H₂) = C₂³

Aliases

C₂³×C₁₉⋊C₃

Fitting, socle, Hall	C₂³×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₂³×C₃

	subgroup	G/H
center, hypercenter	C₂³	C₁₉⋊C₃
commutator, cosocle, hypocenter	C₁₉	C₂³×C₃
Frattini	C₁	G
Fitting, socle	C₂³×C₁₉	C₃
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₂³

64 conjugacy classes of subgroups.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 152

A minimal faithful permutation representation — 3 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(456, 48);