C₁₇×#7021 #16864765

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

Aliases

direct product

C₁₇×#7021

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#95
commutator	C₂×C₄	C₄×C₈×C₁₇
Frattini, cosocle	C₂²×C₄²	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	C₄⋊C₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

380 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 122 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)(20,22)(21,24)(23,25)(26,27)(28,32,33,30)(29,31)(34,35,37,40,39,41,38,36);(19,22,24,23)(26,28)(27,30)(29,33)(31,32)(34,36,38,41,39,40,37,35)

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 9);