C₁₁×Dic₃₁ #13062885

order	1364
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₃₁
unambiguous semidirect product	C₃₁⋊(C₄×C₁₁)

Splittings

derived, Sylow	C₃₁ ⋊ C₄×C₁₁
Hall	C₁₁×C₃₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₃₁
commutator, hypocenter	C₃₁	C₄×C₁₁
Frattini	C₂	C₁₁×D₃₁
Fitting, socle, prime radical	C₂×C₁₁×C₃₁	C₂
cosocle	C₂×C₃₁	C₂×C₁₁
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₁

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 46
transitive degree	μ_t(G) = 1364

A minimal faithful permutation representation — 2 generators on 46 points:

(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46);(12,14,13,15)(17,46)(18,45)(19,44)(20,43)(21,42)(22,41)(23,40)(24,39)(25,38)(26,37)(27,36)(28,35)(29,34)(30,33)(31,32)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₁×Dic₃₁, C₁₁×Dic₉₃, C₁₁×(C₃₁⋊C₃)⋊C₄, …
maximal normal subgroup of	C₃×C₁₁×Dic₃₁, C₁₁×(C₃₁⋊C₃)⋊C₄, C₁₂₁×Dic₃₁, …
maximal quotient of	C₃×C₁₁×Dic₃₁, C₁₁×Dic₉₃, C₁₁×C₃₁⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1364, 2);

C11×Dic31 #13062885