C₂×C₁₇×#2199 #16891291

order	4352
nilpotency class	4
isoclinism	isoclinic class of #2199
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₂×C₁₇×#2199

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂×D₄	C₂⁴×C₁₇
LCS	G ▷ C₂×D₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₁₇ ◁ C₂²×D₄×C₁₇ ◁ G

1392 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 1392 conjugacy classes of subgroups — too many to draw. Only its 222 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 — 4 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)(6,9)(7,10)(8,13)(12,17)(14,16)(15,18);(3,5)(4,8)(6,13)(7,12)(9,11)(10,15)(14,18)(16,17);(5,12)(6,14)(8,15)(11,17)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 26535);