C₁₇×#13366 #16871110

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#13366

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

382 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 61
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(22,23,25,27)(24,28,29,26)(30,31,33,36)(32,40,41,58)(34,46,44,59)(35,49,45,39)(37,53,51,42)(38,55,52,48)(43,60,50,56)(47,57,61,54);(18,19)(20,21)(22,24,25,29)(23,26,27,28)(31,36)(37,51)(38,52)(39,49)(40,58)(46,59)(54,57)(56,60);(19,21)(30,32,33,41)(31,37,36,51)(34,47,44,61)(35,50,45,43)(38,56,52,60)(39,57,49,54)(40,59,58,46)(42,55,53,48)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6354);