C₁₁×Dic₄₇ #14523378

order	2068
isoclinism	isoclinic class of D₄₇
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₄₇
unambiguous semidirect product	C₄₇⋊(C₄×C₁₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₇
commutator, hypocenter	C₄₇	C₄×C₁₁
Frattini	C₂	C₁₁×D₄₇
Fitting, socle, prime radical	C₂×C₁₁×C₄₇	C₂
cosocle	C₂×C₄₇	C₂×C₁₁
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₁

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₇×C₁₁×Dic₄₇, C₁₁×Dic₃₂₉, C₁₁×C₄₇⋊#157, …
maximal normal subgroup of	C₇×C₁₁×Dic₄₇, C₁₂₁×Dic₄₇, C₁₁²×Dic₄₇, …
maximal quotient of	C₇×C₁₁×Dic₄₇, C₁₁×Dic₃₂₉, C₁₁×C₄₇⋊#157, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2068, 3);

C11×Dic47 #14523378