C₁₇×#12974 #16870718

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12974

Subgroups

	subgroup	G/H
center	C₄×C₁₇	B(4,𝔽₂)
commutator	C₂×Q₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
socle	C₂×C₁₇	#1867
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×#41×C₁₇ ◁ G

408 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,29,25,30,23,40)(20,31,34,48,35,47,33,42)(21,28,36,27,22,37,39,46)(26,41,44,38,45,49,43,32);(18,20,24,34,25,35,23,33)(19,26,29,44,30,45,40,43)(21,32,36,41,22,38,39,49)(27,42,37,31,46,48,28,47);(18,21)(19,27)(20,32)(22,25)(23,39)(24,36)(26,42)(28,40)(29,37)(30,46)(31,44)(33,49)(34,41)(35,38)(43,47)(45,48)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5962);