C₇×A₄×C₁₉ #13097629

order	1596
isoclinism	isoclinic class of A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×A₄×C₁₉
unambiguous semidirect product	C₂²⋊(C₃×C₇×C₁₉)

	subgroup	G/H
center, hypercenter	C₇×C₁₉	A₄
commutator, cosocle, hypocenter	C₂²	C₃×C₇×C₁₉
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₉	C₃
LCS	G ▷ C₂²
UCS	C₁ ◁ C₇×C₁₉

20 conjugacy classes of subgroups.

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 532

A minimal faithful permutation representation — 2 generators on 30 points:

(1,2,3,4,5,6,7)(9,10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30);(8,9,10)

532 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 52);