C₁₁×D₈₇ #14274284

order	1914
isoclinism	isoclinic class of D₈₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₈₇
unambiguous semidirect product	C₃⋊(C₁₁×D₂₉)
unambiguous semidirect product	C₂₉⋊(D₃×C₁₁)

Splittings

Fitting, socle, Hall	C₃×C₁₁×C₂₉ ⋊ C₂
derived, Hall	C₃×C₂₉ ⋊ C₂×C₁₁
Hall	C₁₁×C₂₉ ⋊ D₃
Hall	C₃×C₁₁ ⋊ D₂₉
Sylow	C₂₉ ⋊ D₃×C₁₁
Sylow	C₃ ⋊ C₁₁×D₂₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₈₇
commutator, cosocle, hypocenter	C₃×C₂₉	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₃×C₁₁×C₂₉	C₂
LCS	G ▷ C₃×C₂₉
UCS	C₁ ◁ C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 957

A minimal faithful permutation representation — 2 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13,14)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(13,14)(16,43)(17,42)(18,41)(19,40)(20,39)(21,38)(22,37)(23,36)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₃×C₁₁×D₂₉, D₁₁×D₈₇, D₃₃⋊D₂₉, …
maximal normal subgroup of	D₃×C₁₁×D₂₉, D₁₁×D₈₇, D₃₃⋊D₂₉, …
maximal quotient of	C₁₁×Dic₈₇, C₂×C₁₁×D₈₇, C₇×C₁₁×D₈₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1914, 5);

C11×D87 #14274284