#41×C₂₉ #90815

order	464
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	Aut(G) = C₂×C₄×C₇×S₄ (order 1344) · Inn(G) = C₂² · Out(G) = C₂×C₄×D₃×C₇
homology	Abelianization (H₁) = C₂³×C₂₉ · Schur multiplier (H₂) = C₂²

Aliases

	subgroup	G/H
center	C₄×C₂₉	C₂²
commutator, Frattini, cosocle	C₂	C₂³×C₂₉
socle	C₂×C₂₉	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₉ ◁ G

40 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 232

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

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

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(464, 48);