C₃₁×Dic₁₁ #13062884

order	1364
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₃₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃₁×Dic₁₁
unambiguous semidirect product	C₁₁⋊(C₄×C₃₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₁	D₁₁
commutator, hypocenter	C₁₁	C₄×C₃₁
Frattini	C₂	D₁₁×C₃₁
Fitting, socle, prime radical	C₂×C₁₁×C₃₁	C₂
cosocle	C₂×C₁₁	C₂×C₃₁
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₃₁

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);(32,34,33,35)(37,46)(38,45)(39,44)(40,43)(41,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₃₁×Dic₁₁, C₃₁×Dic₃₃, Dic₁₁×C₃₁⋊C₃, …
maximal normal subgroup of	C₃×C₃₁×Dic₁₁, Dic₁₁×C₃₁⋊C₃, C₁₁×C₃₁×Dic₁₁, …
maximal quotient of	C₃×C₃₁×Dic₁₁, C₃₁×Dic₃₃, C₃₁×C₁₁⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1364, 1);

C31×Dic11 #13062884