C₄×#1914 #354281

order	512
nilpotency class	3
isoclinism	isoclinic class of #1913
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄² · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

direct product

C₄×#1914

Subgroups

	subgroup	G/H
center	C₂×C₄	#386
commutator	C₂³	C₂²×C₄²
Frattini, cosocle	C₂³×C₄	C₂⁴
socle	C₂²	C₂×#386
prime radical	C₂×#535	C₂²
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

1975 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 20
transitive degree	μ_t(G) = 64

A minimal faithful permutation representation — 4 generators on 20 points:

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

Conjugacy classes & character table

116 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	AGL(1,𝔽₅)×#1914, C₄×#23872, C₄×#12755, …
maximal normal subgroup of	C₄×#23872, C₄×#12755, #72282928, …
maximal quotient of	AGL(1,𝔽₅)×#1914, #72282907

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 261477);

C4×#1914 #354281

Aliases

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₄×#1914 #354281