AGL(1,𝔽₅)×C₈₁ #13108099

order	1620
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₈₁ · Schur multiplier (H₂) = C₁

Aliases

direct product

AGL(1,𝔽₅)×C₈₁

Splittings

Fitting, Hall	C₅×C₈₁ ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₈₁

Subgroups

	subgroup	G/H
center, hypercenter	C₈₁	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₈₁
Frattini	C₂₇	C₃×AGL(1,𝔽₅)
Fitting	C₅×C₈₁	C₄
socle	C₃×C₅	C₄×C₂₇
prime radical	C₃×D₅	C₂×C₂₇
cosocle	D₅×C₂₇	C₂×C₃
LCS	G ▷ C₅
UCS	C₁ ◁ C₈₁

30 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 86
transitive degree	μ_t(G) = 405

A minimal faithful permutation representation — 2 generators on 86 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);(1,2,3,5,4)

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1620, 5);

AGL(1,𝔽5)×C81 #13108099