Dic₁₁×C₄₇ #14523377

order	2068
isoclinism	isoclinic class of D₁₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₁₁×C₄₇
unambiguous semidirect product	C₁₁⋊(C₄×C₄₇)

Splittings

derived, Sylow	C₁₁ ⋊ C₄×C₄₇
Hall	C₁₁×C₄₇ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄₇	D₁₁
commutator, hypocenter	C₁₁	C₄×C₄₇
Frattini	C₂	D₁₁×C₄₇
Fitting, socle, prime radical	C₂×C₁₁×C₄₇	C₂
cosocle	C₂×C₁₁	C₂×C₄₇
LCS	G ▷ C₁₁
UCS	C₁ ◁ C₂×C₄₇

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 62
transitive degree	μ_t(G) = 2068

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);(1,3,2,4)(6,15)(7,14)(8,13)(9,12)(10,11)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×Dic₁₁×C₄₇, C₄₇×Dic₇₇, C₄₇×C₁₁⋊#157, …
maximal normal subgroup of	C₇×Dic₁₁×C₄₇, C₁₁×Dic₁₁×C₄₇, C₁₃×Dic₁₁×C₄₇, …
maximal quotient of	C₇×Dic₁₁×C₄₇, C₄₇×Dic₇₇, C₄₇×C₁₁⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2068, 2);

Dic11×C47 #14523377