C₁₃×D₄₉ #11929697

order	1274
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃×D₄₉
unambiguous semidirect product	C₄₉⋊(C₂×C₁₃)

Splittings

Fitting, Hall	C₁₃×C₄₉ ⋊ C₂
derived, Sylow	C₄₉ ⋊ C₂×C₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₃	D₄₉
commutator, cosocle, hypocenter	C₄₉	C₂×C₁₃
Frattini	C₇	C₁₃×D₇
Fitting	C₁₃×C₄₉	C₂
socle	C₇×C₁₃	D₇
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₁₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 637

A minimal faithful permutation representation — 2 generators on 62 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62);(15,62)(16,61)(17,60)(18,59)(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

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

Relationships

maximal subgroup of	D₁₃×D₄₉, C₂×C₁₃×D₄₉, C₁₃⋊C₃×D₄₉, …
maximal normal subgroup of	D₁₃×D₄₉, C₂×C₁₃×D₄₉, C₁₃⋊C₃×D₄₉, …
maximal quotient of	C₁₃×Dic₄₉, C₂×C₁₃×D₄₉, C₃×C₁₃×D₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1274, 1);

C13×D49 #11929697