C₁₃⋊C₃×C₄₉ #14274253

order	1911
isoclinism	isoclinic class of C₁₃⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₃⋊C₃×C₄₉
unambiguous semidirect product	C₁₃⋊(C₃×C₄₉)

Splittings

Fitting, Hall	C₁₃×C₄₉ ⋊ C₃
derived, Sylow	C₁₃ ⋊ C₃×C₄₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄₉	C₁₃⋊C₃
commutator, hypocenter	C₁₃	C₃×C₄₉
Frattini	C₇	C₇×C₁₃⋊C₃
Fitting	C₁₃×C₄₉	C₃
socle, cosocle	C₇×C₁₃	C₃×C₇
prime radical	C₇×C₁₃⋊C₃	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:

(2,3,5)(4,7,10)(6,9,8)(11,13,12)(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);(1,2,4,3,6,10,7,11,13,5,8,12,9)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₉×D₁₃⋊C₃, C₁₃⋊C₃×D₄₉, (C₁₃⋊C₃)⋊D₄₉, …
maximal normal subgroup of	C₄₉×D₁₃⋊C₃, C₁₃⋊C₃×D₄₉, (C₁₃⋊C₃)⋊D₄₉, …
maximal quotient of	C₂×C₁₃⋊C₃×C₄₉, C₁₁×C₁₃⋊C₃×C₄₉, C₄₉×C₁₆₉⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1911, 2);

C13⋊C3×C49 #14274253