C₂×C₁₇×#1304 #16865843

order	4352
nilpotency class	3
isoclinism	isoclinic class of #1304
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₁₇×#1304

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₇	#95
commutator	C₂³	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁵	C₂³×C₁₇
prime radical	C₂⁶×C₁₇	C₂²
LCS	G ▷ C₂³ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂⁶×C₁₇ ◁ G

2414 conjugacy classes of subgroups; only the 286 normal subgroups are shown.

normal subgroups only

This group has 2414 conjugacy classes of subgroups — too many to draw. Only its 286 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) = 35
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 35 points:

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

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, 1087);