C₁₇×#8541 #16866285

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8541
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₇×#8541

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂²×C₁₇×#120	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂⁵×C₁₇ ◁ G

2618 conjugacy classes of subgroups; only the 174 normal subgroups are shown.

normal subgroups only

This group has 2618 conjugacy classes of subgroups — too many to draw. Only its 174 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) = 33
transitive degree	μ_t(G) = 272

A minimal faithful permutation representation — 3 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,25)(21,23,26,30)(22,24,27,31)(28,29,32,33);(19,23)(20,26)(24,29)(27,32);(19,24)(20,27)(23,29)(26,32)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1529);