C₁₇×#11477 #16869221

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#11477

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×D₄×C₁₇	C₂×C₄
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₄×D₄×C₁₇ ◁ G

480 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 134 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 — 3 generators on 41 points:

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

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, 4465);