C₁₇×#7034 #16864778

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7034

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#95
commutator	C₂³	C₄×C₈×C₁₇
Frattini, cosocle	C₂²×C₄²	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	C₄²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

406 conjugacy classes of subgroups; only the 134 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 134 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) = 41
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(27,30)(28,32)(34,35,36,38,37,39,40,41);(18,20)(19,22)(21,25)(23,24)(26,27,28,31,29,30,32,33)

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, 22);