C₁₃×Dic₄₁ #14523816

order	2132
isoclinism	isoclinic class of D₄₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₃×Dic₄₁

Splittings

derived, Sylow	C₄₁ ⋊ C₄×C₁₃
Hall	C₁₃×C₄₁ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₃	D₄₁
commutator, hypocenter	C₄₁	C₄×C₁₃
Frattini	C₂	C₁₃×D₄₁
Fitting, socle, prime radical	C₂×C₁₃×C₄₁	C₂
cosocle	C₂×C₄₁	C₂×C₁₃
LCS	G ▷ C₄₁
UCS	C₁ ◁ C₂×C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 58
transitive degree	μ_t(G) = 2132

A minimal faithful permutation representation — 2 generators on 58 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58);(14,16,15,17)(19,58)(20,57)(21,56)(22,55)(23,54)(24,53)(25,52)(26,51)(27,50)(28,49)(29,48)(30,47)(31,46)(32,45)(33,44)(34,43)(35,42)(36,41)(37,40)(38,39)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₃×Dic₄₁, C₁₃×Dic₂₈₇, C₁₃×#13093288, …
maximal normal subgroup of	C₇×C₁₃×Dic₄₁, C₁₁×C₁₃×Dic₄₁, Dic₄₁×C₁₆₉, …
maximal quotient of	C₇×C₁₃×Dic₄₁, C₁₃×Dic₂₈₇, C₁₃×#13093288, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2132, 3);

C13×Dic41 #14523816