C₁₇×#7206 #16864950

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

Aliases

direct product

C₁₇×#7206

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₇
socle	C₂²×C₁₇	#342
prime radical	C₂³×C₁₇	#95
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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) = 2176

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)(18,19,21,24,23,25,22,20)(26,27,29,33,30,34,38,41)(28,32,35,40,36,31,37,39);(18,20,22,25,23,24,21,19)(27,31,34,32)(33,40,41,39)

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, 194);