C₁₇×AGL(1,𝔽₅)×C₅₉ #34095403

order	20060
isoclinism	isoclinic class of AGL(1,𝔽₅)
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₇×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product

C₁₇×AGL(1,𝔽₅)×C₅₉

Splittings

Fitting, socle, Hall	C₅×C₁₇×C₅₉ ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₁₇×C₅₉
Hall	C₅×C₅₉ ⋊ C₄×C₁₇
Hall	C₅×C₁₇ ⋊ C₄×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₇×C₅₉	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₁₇×C₅₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₇×C₅₉	C₄
prime radical	D₅×C₁₇×C₅₉	C₂
cosocle	D₅	C₂×C₁₇×C₅₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₇×C₅₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 81
transitive degree	μ_t(G) = 5015

A minimal faithful permutation representation — 2 generators on 81 points:

(2,5,4,3)(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);(1,2,3,5,4)

Conjugacy classes & character table

5015 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20060, 13);

C17×AGL(1,𝔽5)×C59 #34095403