C₁₇×#7134 #16864878

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1366
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#7134

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#333
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	C₄³	C₂²×C₁₇
socle	C₂×C₁₇	#1272
prime radical	C₂³×C₁₇	#99
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₄³×C₁₇ ◁ G

230 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 70 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)(20,27,29,23,28,32,30,33)(21,24)(22,26)(25,31);(18,20,22,28)(19,23)(21,30,31,29)(24,27)(25,32)(26,33)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 122);