Dic₁₁×C₄₉ #14524148

order	2156
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₁₁×C₄₉
unambiguous semidirect product	C₁₁⋊(C₄×C₄₉)

Splittings

derived, Sylow	C₁₁ ⋊ C₄×C₄₉
Hall	C₁₁×C₄₉ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₉	D₁₁
commutator, hypocenter	C₁₁	C₄×C₄₉
Frattini	C₂×C₇	C₇×D₁₁
Fitting	C₂×C₁₁×C₄₉	C₂
socle, prime radical, cosocle	C₂×C₇×C₁₁	C₂×C₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₄₉

18 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 64
transitive degree	μ_t(G) = 2156

A minimal faithful permutation representation — 2 generators on 64 points:

(1,2)(3,4)(5,6,7,8,9,10,11,12,13,14,15)(16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₄₉×C₁₁⋊#157, C₄₉×Dic₁₂₁, C₁₁×Dic₁₁×C₄₉, …
maximal normal subgroup of	C₁₁×Dic₁₁×C₄₉, C₁₃×Dic₁₁×C₄₉, C₁₇×Dic₁₁×C₄₉
maximal quotient of	C₄₉×C₁₁⋊#157, C₄₉×Dic₁₂₁, C₁₁×Dic₁₁×C₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2156, 3);

Dic11×C49 #14524148