C₇×D₁₄₃ #14523005

order	2002
isoclinism	isoclinic class of D₁₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₄₃
unambiguous semidirect product	C₁₁⋊(C₇×D₁₃)
unambiguous semidirect product	C₁₃⋊(C₇×D₁₁)

Splittings

Fitting, socle, Hall	C₇×C₁₁×C₁₃ ⋊ C₂
derived, Hall	C₁₁×C₁₃ ⋊ C₂×C₇
Hall	C₇×C₁₃ ⋊ D₁₁
Hall	C₇×C₁₁ ⋊ D₁₃
Sylow	C₁₃ ⋊ C₇×D₁₁
Sylow	C₁₁ ⋊ C₇×D₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇	D₁₄₃
commutator, cosocle, hypocenter	C₁₁×C₁₃	C₂×C₇
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₁₃	C₂
LCS	G ▷ C₁₁×C₁₃
UCS	C₁ ◁ C₇

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1001

A minimal faithful permutation representation — 2 generators on 31 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);(9,18)(10,17)(11,16)(12,15)(13,14)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×D₁₁×D₁₃, D₇×D₁₄₃, D₇₇⋊D₁₃, …
maximal normal subgroup of	C₇×D₁₁×D₁₃, D₇×D₁₄₃, D₇₇⋊D₁₃, …
maximal quotient of	C₇×Dic₁₄₃, C₂×C₇×D₁₄₃, C₄₉×D₁₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2002, 4);

C7×D143 #14523005