C₁₇×#12107 #16869851

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12102
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12107

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3191	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₂²⋊C₈ ◁ G

428 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 1088

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

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, 5095);