SU(4,𝔽₂) #72209939

order	25920
isoclinism	isoclinic class of SU(4,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₁ · Schur multiplier (H₂) = C₂

Aliases

projective symplectic	PSp(4,𝔽₃)
omega	Ω(5,𝔽₃)
special unitary	SU(4,𝔽₂)
projective special unitary	PSU(4,𝔽₂)

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, hypocenter	G	C₁
LCS	G
UCS	C₁

116 conjugacy classes of subgroups; only the 2 normal subgroups are shown.

normal subgroups only

This group has 116 conjugacy classes of subgroups — too many to draw. Only its 2 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

Permutation generators:

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

Conjugacy classes & character table

20 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	SO(5,𝔽₃)
maximal normal subgroup of	SO(5,𝔽₃)
maximal quotient of	Sp(4,𝔽₃)

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from its permutation generators:

gap> G := Group((1,2)(3,5)(4,7)(6,9)(8,11)(10,13)(12,17)(15,20)(16,18)(19,23)(21,24)(22,26), (2,3,6,8,4)(7,9,12,14,10)(11,15,21,22,16)(13,18,24,25,19)(17,23,27,26,20));