C₁₇×#11752 #16869496

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11704
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#11752

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	C₂×SD₁₆
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

320 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 118 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) = 2176

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

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, 4740);