C₁₇×#7489 #16865233

order	4352
nilpotency class	5
isoclinism	isoclinic class of #1404
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#7489

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	AΣL(1,𝔽₁₆)
commutator	C₂×Q₈	C₄²×C₁₇
Frattini, cosocle	C₂×#124	C₂²×C₁₇
prime radical	C₂²×D₄×C₁₇	D₄
LCS	G ▷ C₂×Q₈ ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#124 ◁ G

302 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,24,28)(25,34,35,31)(26,30,33,37)(27,36,29,32);(18,19,20,21)(22,23)(24,31)(25,34)(26,30)(27,33)(28,32)(29,36)(35,37)

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, 477);