C₇×D₁₁×C₈₃ #27165287

order	12782
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₈₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×D₁₁×C₈₃
unambiguous semidirect product	C₁₁⋊(C₂×C₇×C₈₃)

Splittings

Fitting, socle, Hall	C₇×C₁₁×C₈₃ ⋊ C₂
derived, Sylow	C₁₁ ⋊ C₂×C₇×C₈₃
Hall	C₁₁×C₈₃ ⋊ C₂×C₇
Hall	C₇×C₁₁ ⋊ C₂×C₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₈₃	D₁₁
commutator, cosocle, hypocenter	C₁₁	C₂×C₇×C₈₃
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₈₃	C₂
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₇×C₈₃

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6391

A minimal faithful permutation representation — 2 generators on 101 points:

(2,3)(4,5)(6,7)(8,9)(10,11)(12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94)(95,96,97,98,99,100,101);(1,2,4,6,8,10,11,9,7,5,3)

Conjugacy classes & character table

4067 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₁×D₈₃, D₇×D₁₁×C₈₃, D₁₁×D₅₈₁, …
maximal normal subgroup of	C₇×D₁₁×D₈₃, D₇×D₁₁×C₈₃, D₁₁×D₅₈₁, …
maximal quotient of	C₇×Dic₁₁×C₈₃, C₂×C₇×D₁₁×C₈₃, C₃×C₇×D₁₁×C₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12782, 3);

C7×D11×C83 #27165287