C₁₁×Dic₄₉ #14524147

order	2156
isoclinism	isoclinic class of D₄₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₄₉
unambiguous semidirect product	C₄₉⋊(C₄×C₁₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₄₉
commutator, hypocenter	C₄₉	C₄×C₁₁
Frattini	C₂×C₇	C₁₁×D₇
Fitting	C₂×C₁₁×C₄₉	C₂
socle, prime radical	C₂×C₇×C₁₁	D₇
cosocle	C₂×C₄₉	C₂×C₁₁
LCS	G ▷ C₄₉
UCS	C₁ ◁ C₂×C₁₁

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁×C₄₉⋊#157, C₁₂₁×Dic₄₉, C₁₁²×Dic₄₉, …
maximal normal subgroup of	C₁₂₁×Dic₄₉, C₁₁²×Dic₄₉, C₁₁×C₁₃×Dic₄₉, …
maximal quotient of	C₁₁×C₄₉⋊#157, C₁₂₁×Dic₄₉, C₁₁²×Dic₄₉, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2156, 2);

C11×Dic49 #14524147