C₁₇×#12697 #16870441

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11508
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵×C₄

Aliases

direct product

C₁₇×#12697

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#99
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×D₄	C₂³×C₁₇
prime radical	C₂×C₁₇×#535	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×#41×C₁₇ ◁ G

1182 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 37
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,21)(22,23)(24,28)(25,29,33,27)(26,30)(31,36)(32,35,37,34);(23,27)(24,31)(25,33)(28,35)(29,30)(34,36);(19,21)(22,24,26,31)(23,28,30,36)(25,32,33,37)(27,34,29,35)

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, 5685);