Finite Group Databasebeta

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#100×PSU(3,𝔽₂)⋊C₃ #72220475

order	6912
automorphism	?
homology	Abelianization (H₁) = C₂×C₃×C₄ · Schur multiplier (H₂) = C₂×C₃

Aliases

#100×PSU(3,𝔽₂)⋊C₃

Splittings

C₃²×#100 ⋊ SL(2,𝔽₃)

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊C₄×PSU(3,𝔽₂)⋊C₃
commutator	C₂²×PSU(3,𝔽₂)	C₂×C₃×C₄
Frattini	C₂×C₄	C₂²×PSU(3,𝔽₂)⋊C₃
Fitting	C₃²×#100	SL(2,𝔽₃)
socle	C₂×C₃²	C₂²⋊C₄×SL(2,𝔽₃)
prime radical	C₂×D₄×PSU(3,𝔽₂)⋊C₃	C₂
cosocle	C₂×C₄×PSU(3,𝔽₂)	C₂²×C₃
hypercenter	#100	PSU(3,𝔽₂)⋊C₃
hypocenter	PSU(3,𝔽₂)	C₃×#100
LCS	G ▷ C₂²×PSU(3,𝔽₂) ▷ C₂×PSU(3,𝔽₂) ▷ PSU(3,𝔽₂)
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

1018 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 1018 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

110 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.