C₁₇×#7126 #16864870

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7126

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#327
commutator	C₂×C₈	C₂×C₈×C₁₇
Frattini, cosocle	C₂×#97	C₂²×C₁₇
prime radical	C₂³×C₁₇	#102
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

202 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 202 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 1088

A minimal faithful permutation representation — 2 generators on 41 points:

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 114);