C₁₇×#12076 #16869820

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12076

Subgroups

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

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

normal subgroups only

This group has 210 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) = 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)(18,19,21,20,22,23,25,24)(26,27,30,34)(28,36,37,55)(29,40,43,54)(31,45,42,35)(32,47,48,38)(33,50,52,44)(39,56,46,51)(41,53,57,49);(26,28,30,37)(27,32,34,48)(29,41,43,57)(31,46,42,39)(33,51,52,56)(35,53,45,49)(36,54,55,40)(38,50,47,44);(18,20,21,23,22,24,25,19)(28,37)(32,48)(36,55)(38,47)(39,46)(41,57)(49,53)(51,56)

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, 5064);