Finite Group Databasebeta

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#100×ΓL(1,𝔽₁₆) #14295430

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄² · Schur multiplier (H₂) = C₂²×C₄

Aliases

#100×ΓL(1,𝔽₁₆)

Splittings

Fitting	C₃×C₅×#100 ⋊ C₄
Hall	C₃×C₅ ⋊ C₄×#100
Sylow	C₅ ⋊ Dic₃×#100
Sylow	C₃ ⋊ AGL(1,𝔽₅)×#100

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊C₄×ΓL(1,𝔽₁₆)
commutator	C₂²×C₃×C₅	C₂×C₄²
Frattini	C₂×C₄	C₂²×ΓL(1,𝔽₁₆)
Fitting	C₃×C₅×#100	C₄
socle	C₂×C₃×C₅	C₄×C₂²⋊C₄
prime radical	C₂×C₃×D₄×D₅	C₂²
cosocle	C₂×C₃×C₄×D₅	C₂³
hypercenter	#100	ΓL(1,𝔽₁₆)
hypocenter	C₃×C₅	C₄×#100
LCS	G ▷ C₂²×C₃×C₅ ▷ C₂×C₃×C₅ ▷ C₃×C₅
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ #100

720 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 720 conjugacy classes of subgroups — too many to draw. Only its 143 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 120

Conjugacy classes & character table

99 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	ΓL(1,𝔽₁₆)×#453, D₃×AGL(1,𝔽₅)×#100, #72230884
maximal normal subgroup of	ΓL(1,𝔽₁₆)×#453, D₃×AGL(1,𝔽₅)×#100, #72230884

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 21128);