C₇×C₁₁×D₈₃ #27165286

order	12782
isoclinism	isoclinic class of D₈₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₁₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₁₁×D₈₃
unambiguous semidirect product	C₈₃⋊(C₂×C₇×C₁₁)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₁₁	D₈₃
commutator, cosocle, hypocenter	C₈₃	C₂×C₇×C₁₁
Frattini	C₁	G
Fitting, socle	C₇×C₁₁×C₈₃	C₂
LCS	G ▷ C₈₃
UCS	C₁ ◁ C₇×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)(84,85,86,87,88,89,90,91,92,93,94)(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)

Conjugacy classes & character table

3311 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₇×D₁₁×D₈₃, C₁₁×D₇×D₈₃, D₇₇×D₈₃, …
maximal normal subgroup of	C₇×D₁₁×D₈₃, C₁₁×D₇×D₈₃, D₇₇×D₈₃, …
maximal quotient of	C₇×C₁₁×Dic₈₃, C₂×C₇×C₁₁×D₈₃, C₃×C₇×C₁₁×D₈₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12782, 2);

C7×C11×D83 #27165286