C₁₁×D₅₈₁ #27165290

order	12782
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₁×D₅₈₁
unambiguous semidirect product	C₇⋊(C₁₁×D₈₃)
unambiguous semidirect product	C₈₃⋊(C₁₁×D₇)

Splittings

Fitting, socle, Hall	C₇×C₁₁×C₈₃ ⋊ C₂
derived, Hall	C₇×C₈₃ ⋊ C₂×C₁₁
Hall	C₁₁×C₈₃ ⋊ D₇
Sylow	C₈₃ ⋊ C₁₁×D₇
Hall	C₇×C₁₁ ⋊ D₈₃
Sylow	C₇ ⋊ C₁₁×D₈₃

Subgroups

	subgroup	G/H
center, hypercenter	C₁₁	D₅₈₁
commutator, cosocle, hypocenter	C₇×C₈₃	C₂×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₈₃	C₂
LCS	G ▷ C₇×C₈₃
UCS	C₁ ◁ C₁₁

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 101
transitive degree	μ_t(G) = 6391

A minimal faithful permutation representation — 2 generators on 101 points:

(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)(64,65)(66,67)(68,69)(70,71)(72,73)(74,75)(76,77)(78,79)(80,81)(82,83)(85,86)(87,88)(89,90)(91,92,93,94,95,96,97,98,99,100,101);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,83,81,79,77,75,73,71,69,67,65,63,61,59,57,55,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(84,85,87,89,90,88,86)

Conjugacy classes & character table

3212 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₁₁×D₇×D₈₃, D₁₁×D₅₈₁, D₇₇⋊D₈₃, …
maximal normal subgroup of	C₁₁×D₇×D₈₃, D₁₁×D₅₈₁, D₇₇⋊D₈₃, …
maximal quotient of	C₁₁×Dic₅₈₁, C₂×C₁₁×D₅₈₁, C₃×C₁₁×D₅₈₁, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12782, 6);

C11×D581 #27165290