C₁₇×#7487 #16865231

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7487

Subgroups

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

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

normal subgroups only

This group has 298 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)(22,23,26,30,27,24,25,33)(28,34,35,29,37,31,36,32);(18,19,20,21)(22,24,27,23)(25,32,26,29)(28,31,37,34)(30,35,33,36)

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, 475);