C₁₃×Dic₃₁ #13108019

order	1612
isoclinism	isoclinic class of D₃₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×Dic₃₁
unambiguous semidirect product	C₃₁⋊(C₄×C₁₃)

Splittings

derived, Sylow	C₃₁ ⋊ C₄×C₁₃
Hall	C₁₃×C₃₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₃₁
commutator, hypocenter	C₃₁	C₄×C₁₃
Frattini	C₂	C₁₃×D₃₁
Fitting, socle, prime radical	C₂×C₁₃×C₃₁	C₂
cosocle	C₂×C₃₁	C₂×C₁₃
LCS	G ▷ C₃₁
UCS	C₁ ◁ C₂×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 48
transitive degree	μ_t(G) = 1612

A minimal faithful permutation representation — 2 generators on 48 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48);(14,16,15,17)(19,48)(20,47)(21,46)(22,45)(23,44)(24,43)(25,42)(26,41)(27,40)(28,39)(29,38)(30,37)(31,36)(32,35)(33,34)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₁₃×Dic₃₁, C₁₃×Dic₉₃, C₁₃×(C₃₁⋊C₃)⋊C₄, …
maximal normal subgroup of	C₃×C₁₃×Dic₃₁, C₁₃×(C₃₁⋊C₃)⋊C₄, C₁₃⋊C₃×Dic₃₁, …
maximal quotient of	C₃×C₁₃×Dic₃₁, C₁₃×Dic₉₃, C₇×C₁₃×Dic₃₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1612, 2);

C13×Dic31 #13108019