C₂₉×C₂²⋊A₄ #13063683

order	1392
isoclinism	isoclinic class of C₂²⋊A₄
automorphism	?
homology	Abelianization (H₁) = C₃×C₂₉ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product	C₂₉×C₂²⋊A₄
unambiguous semidirect product	C₂²⋊(A₄×C₂₉)
unambiguous semidirect product	(C₂²×C₂₉)⋊A₄

Fitting, socle, Hall	C₂⁴×C₂₉ ⋊ C₃
derived, Sylow	C₂⁴ ⋊ C₃×C₂₉

	subgroup	G/H
center, hypercenter	C₂₉	C₂²⋊A₄
commutator, cosocle, hypocenter	C₂⁴	C₃×C₂₉
Frattini	C₁	G
Fitting, socle	C₂⁴×C₂₉	C₃
LCS	G ▷ C₂⁴
UCS	C₁ ◁ C₂₉

68 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 348

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(31,32,33)(35,36,37);(34,37)(35,36);(30,33)(31,32)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1392, 194);