C₁₇×#7426 #16865170

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7426
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7426

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1351
commutator	C₂×C₂²⋊C₄	C₂×C₄×C₁₇
Frattini, cosocle	#379	C₂²×C₁₇
prime radical	C₂⁵×C₁₇	D₄
LCS	G ▷ C₂×C₂²⋊C₄ ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂⁴×C₁₇ ◁ C₁₇×#379 ◁ G

332 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 42 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 — 2 generators on 33 points:

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

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 414);