C₁₃×D₄₇ #11927424

order	1222
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₄₇
unambiguous semidirect product	C₄₇⋊(C₂×C₁₃)

Splittings

Fitting, socle, Hall	C₁₃×C₄₇ ⋊ C₂
derived, Sylow	C₄₇ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂×C₁₃
Frattini	C₁	G
Fitting, socle	C₁₃×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₁₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 611

A minimal faithful permutation representation — 2 generators on 60 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60);(15,60)(16,59)(17,58)(18,57)(19,56)(20,55)(21,54)(22,53)(23,52)(24,51)(25,50)(26,49)(27,48)(28,47)(29,46)(30,45)(31,44)(32,43)(33,42)(34,41)(35,40)(36,39)(37,38)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₁₃×D₄₇, C₂×C₁₃×D₄₇, C₃×C₁₃×D₄₇, …
maximal normal subgroup of	D₁₃×D₄₇, C₂×C₁₃×D₄₇, C₃×C₁₃×D₄₇, …
maximal quotient of	C₁₃×Dic₄₇, C₂×C₁₃×D₄₇, C₃×C₁₃×D₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1222, 2);

C13×D47 #11927424