D₁₃×C₄₇ #11927423

order	1222
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₃×C₄₇
unambiguous semidirect product	C₁₃⋊(C₂×C₄₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₁₃
commutator, cosocle, hypocenter	C₁₃	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₁₃×C₄₇	C₂
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄₇

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);(2,13)(3,12)(4,11)(5,10)(6,9)(7,8)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₇×#261, C₄₇⋊#261, D₁₃×D₄₇, …
maximal normal subgroup of	C₄₇×#261, C₄₇⋊#261, D₁₃×D₄₇, …
maximal quotient of	C₄₇×Dic₁₃, C₂×D₁₃×C₄₇, C₃×D₁₃×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1222, 1);

D13×C47 #11927423