C₁₁×D₉₁ #14523007

order	2002
isoclinism	isoclinic class of D₉₁
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₉₁
unambiguous semidirect product	C₇⋊(C₁₁×D₁₃)
unambiguous semidirect product	C₁₃⋊(C₁₁×D₇)

Splittings

Fitting, socle, Hall	C₇×C₁₁×C₁₃ ⋊ C₂
derived, Hall	C₇×C₁₃ ⋊ C₂×C₁₁
Hall	C₁₁×C₁₃ ⋊ D₇
Hall	C₇×C₁₁ ⋊ D₁₃
Sylow	C₁₃ ⋊ C₁₁×D₇
Sylow	C₇ ⋊ C₁₁×D₁₃

Subgroups

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

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1001

A minimal faithful permutation representation — 2 generators on 31 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);(13,18)(14,17)(15,16)(20,31)(21,30)(22,29)(23,28)(24,27)(25,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₁₁×D₇×D₁₃, D₁₁×D₉₁, D₇₇⋊D₁₃, …
maximal normal subgroup of	C₁₁×D₇×D₁₃, D₁₁×D₉₁, D₇₇⋊D₁₃, …
maximal quotient of	C₁₁×Dic₉₁, C₂×C₁₁×D₉₁, C₁₁×D₆₃₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2002, 6);

C11×D91 #14523007