C₁₇×#12073 #16869817

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

Aliases

direct product

C₁₇×#12073

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂×D₈
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂²×C₁₇	C₄×D₈
prime radical	C₂×C₁₇×D₁₆	C₄
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₈²×C₁₇ ◁ G

240 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 98 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 — 3 generators on 41 points:

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

Conjugacy classes & character table

986 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5061);