C₁₇×#7116 #16864860

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1355
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7116

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#329
commutator	C₄²	C₂×C₈×C₁₇
Frattini, cosocle	C₂×#97	C₂²×C₁₇
prime radical	C₂×C₁₇×#127	C₄
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

282 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 41
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 2 generators on 41 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,25,22)(21,23)(26,27,28,34,30,33,36,40,31,35,37,41,29,32,38,39);(18,20)(19,22)(21,25)(23,24)(27,32)(28,36)(29,30)(33,35)(34,41)(37,38)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 104);