C₁₇×#11431 #16869175

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₇×#11431

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂×C₄	C₂²×C₈×C₁₇
Frattini, cosocle	C₂×C₄⋊C₄	C₂³×C₁₇
socle	C₂²×C₁₇	C₂×#99
prime radical	C₂²×#41×C₁₇	C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

602 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 602 conjugacy classes of subgroups — too many to draw. Only its 142 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 — 3 generators on 41 points:

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

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, 4419);