C₁₇×#13560 #16871304

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#13560

Subgroups

	subgroup	G/H
center	C₄×C₁₇	AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₂²×C₄×C₁₇
Frattini, cosocle	#127	C₂³×C₁₇
socle	C₂×C₁₇	C₂×AΣL(1,𝔽₁₆)
prime radical	C₁₇×#3018	C₂
LCS	G ▷ C₂×D₄ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#532 ◁ G

486 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 90 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,29,31,24)(21,25)(22,27,36,26)(23,28)(30,43,44,37)(32,42,35,38)(33,40,47,39)(34,41)(45,49,46,48);(18,20)(19,24)(21,30)(22,35)(23,32)(25,37)(26,29)(27,42)(28,38)(31,36)(33,46)(34,45)(39,43)(40,49)(41,48)(44,47);(18,21,23,34)(19,25,28,41)(20,30,32,45)(22,33,36,47)(24,37,38,48)(26,39,27,40)(29,43,42,49)(31,44,35,46)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6548);