C₁₇×#13306 #16871050

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13306

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₂⁴×C₁₇	D₈
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

566 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 138 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)(18,19)(20,21)(26,27,31,35)(28,36,39,55)(29,40,44,54)(30,45,42,34)(32,47,49,37)(33,50,52,43)(38,56,46,51)(41,53,57,48);(22,23)(24,25)(26,28,31,39)(27,32,35,49)(29,41,44,57)(30,46,42,38)(33,51,52,56)(34,53,45,48)(36,54,55,40)(37,50,47,43);(19,21)(23,25)

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, 6294);