C₁₁×Dic₉₁ #16860705

order	4004
isoclinism	isoclinic class of D₉₁
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×Dic₉₁
unambiguous semidirect product	C₇⋊(C₁₁×Dic₁₃)

Splittings

derived, Hall	C₇×C₁₃ ⋊ C₄×C₁₁
Hall	C₇×C₁₁×C₁₃ ⋊ C₄
Hall	C₁₁×C₁₃ ⋊ Dic₇
Hall	C₇×C₁₁ ⋊ Dic₁₃
Sylow	C₁₃ ⋊ C₁₁×Dic₇
Sylow	C₇ ⋊ C₁₁×Dic₁₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₁	D₉₁
commutator, hypocenter	C₇×C₁₃	C₄×C₁₁
Frattini	C₂	C₁₁×D₉₁
Fitting, socle, prime radical	C₂×C₇×C₁₁×C₁₃	C₂
cosocle	C₂×C₇×C₁₃	C₂×C₁₁
LCS	G ▷ C₇×C₁₃
UCS	C₁ ◁ C₂×C₁₁

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 35
transitive degree	μ_t(G) = 4004

A minimal faithful permutation representation — 2 generators on 35 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);(12,14,13,15)(17,22)(18,21)(19,20)(24,35)(25,34)(26,33)(27,32)(28,31)(29,30)

Conjugacy classes & character table

1034 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₁×Dic₉₁, C₁₁×Dic₂₇₃, C₁₁×#11763955, …
maximal normal subgroup of	C₃×C₁₁×Dic₉₁, C₁₁×#11763955, C₁₁×ΓL(1,𝔽₈)⋊Dic₁₃, …
maximal quotient of	C₃×C₁₁×Dic₉₁, C₁₁×Dic₂₇₃, C₅×C₁₁×Dic₉₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4004, 6);

C11×Dic91 #16860705