C₁₇×#13564 #16871308

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13564

Subgroups

	subgroup	G/H
center	C₄×C₁₇	AΣL(1,𝔽₁₆)
commutator	C₂×D₄	C₂²×C₄×C₁₇
Frattini, cosocle	#124	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

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

normal subgroups only

This group has 494 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,27,24,20,28,31)(21,25,32,26,23,29,33,30);(18,20)(19,24)(21,29)(22,30)(23,25)(26,28)(27,32)(31,33);(18,21,24,23)(19,25,20,29)(22,32,28,33)(26,31,30,27)

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, 6552);