C₁₇×#23467 #16881211

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#23467

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#120
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂×#120
prime radical	C₂⁵×C₁₇	C₂³
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

1378 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1378 conjugacy classes of subgroups — too many to draw. Only its 334 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 4 generators on 41 points:

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

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 16455);