C₂×D₁₀₀₁ #16860720

order	4004
automorphism	Aut(G) order 1441440
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

dihedral	D₂₀₀₂
direct product	C₂×D₁₀₀₁
unambiguous semidirect product	(C₂×C₇)⋊D₁₄₃
unambiguous semidirect product	(C₂×C₁₁)⋊D₉₁
unambiguous semidirect product	(C₂×C₁₃)⋊D₇₇

Splittings

Fitting, socle	C₂×C₇×C₁₁×C₁₃ ⋊ C₂
derived, Hall	C₇×C₁₁×C₁₃ ⋊ C₂²
Hall	C₁₁×C₁₃ ⋊ C₂×D₇
Hall	C₇×C₁₃ ⋊ C₂×D₁₁
Hall	C₇×C₁₁ ⋊ C₂×D₁₃
Sylow	C₁₃ ⋊ C₂×D₇₇
Sylow	C₁₁ ⋊ C₂×D₉₁
Sylow	C₇ ⋊ C₂×D₁₄₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂	D₁₀₀₁
commutator, cosocle, hypocenter	C₇×C₁₁×C₁₃	C₂²
Frattini	C₁	G
Fitting, socle	C₂×C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₇×C₁₁×C₁₃
UCS	C₁ ◁ C₂

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 2002

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

1004 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₁₁⋊#10587722, C₂×C₁₁⋊#10587723, C₂×C₁₁⋊(ΓL(1,𝔽₈)⋊D₁₃), …
maximal normal subgroup of	C₂×C₁₁⋊#10587722, C₂×C₁₁⋊#10587723, C₂×C₁₁⋊(ΓL(1,𝔽₈)⋊D₁₃), …
maximal quotient of	D₃×D₁₀₀₁, C₂×D₃₀₀₃, C₂×C₃×D₁₀₀₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4004, 21);

C2×D1001 #16860720