C₇×C₄₁×D₃₅ #34095604

order	20090
isoclinism	isoclinic class of D₃₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₇×C₄₁ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₇×C₄₁×D₃₅
unambiguous semidirect product	C₅⋊(C₇×D₇×C₄₁)
unambiguous semidirect product	C₇⋊(C₇×D₅×C₄₁)

Splittings

Fitting, socle, Hall	C₅×C₇²×C₄₁ ⋊ C₂
derived	C₅×C₇ ⋊ C₂×C₇×C₄₁
Hall	C₇²×C₄₁ ⋊ D₅
Hall	C₅×C₇² ⋊ C₂×C₄₁
Hall	C₅×C₄₁ ⋊ C₇×D₇
Sylow	C₇² ⋊ D₅×C₄₁
Sylow	C₅ ⋊ C₇×D₇×C₄₁

Subgroups

	subgroup	G/H
center, hypercenter	C₇×C₄₁	D₃₅
commutator, cosocle, hypocenter	C₅×C₇	C₂×C₇×C₄₁
Frattini	C₁	G
Fitting, socle	C₅×C₇²×C₄₁	C₂
LCS	G ▷ C₅×C₇
UCS	C₁ ◁ C₇×C₄₁

44 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 60
transitive degree	μ_t(G) = 2870

A minimal faithful permutation representation — 2 generators on 60 points:

(1,2,3,4,5,6,7)(9,10)(11,12)(13,14)(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);(8,9,11,13,14,12,10)(15,16,18,19,17)

Conjugacy classes & character table

5453 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20090, 27);

C7×C41×D35 #34095604