C₁₇×#12066 #16869810

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

Aliases

direct product

C₁₇×#12066

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#442
commutator	C₈	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#322 ◁ G

214 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 214 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 57
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,24,22,20,23,25)(26,27,30,36,32,37,31,34)(28,38,40,55,42,56,41,52)(29,43,46,53,45,51,47,35)(33,48,49,39,50,44,54,57);(26,28,32,42)(27,33,37,50)(29,44,45,48)(30,41,31,40)(34,49,36,54)(35,52,53,55)(38,43,56,51)(39,47,57,46);(18,20,21,25,22,19,23,24)(27,34,37,36)(29,45)(33,49,50,54)(35,43,53,51)(38,52,56,55)(39,57)(44,48)(46,47)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5054);