D₁₃×C₄₉ #11929698

order	1274
isoclinism	isoclinic class of D₁₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₁₃×C₄₉
unambiguous semidirect product	C₁₃⋊(C₂×C₄₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	D₁₃
commutator, hypocenter	C₁₃	C₂×C₄₉
Frattini	C₇	C₇×D₁₃
Fitting	C₁₃×C₄₉	C₂
socle, cosocle	C₇×C₁₃	C₂×C₇
prime radical	C₇×D₁₃	C₇
LCS	G ▷ C₁₃
UCS	C₁ ◁ C₄₉

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₉×#261, C₄₉⋊#261, D₁₃×D₄₉, …
maximal normal subgroup of	C₄₉×#261, C₄₉⋊#261, D₁₃×D₄₉, …
maximal quotient of	C₄₉×Dic₁₃, C₂×D₁₃×C₄₉, C₃×D₁₃×C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1274, 2);

D13×C49 #11929698