C₁₇×#7124 #16864868

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7124

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂²×C₄	C₂×C₈×C₁₇
Frattini, cosocle	C₂×#97	C₂²×C₁₇
socle	C₂²×C₁₇	#324
prime radical	C₂³×C₁₇	C₂²⋊C₈
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#97 ◁ G

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

normal subgroups only

This group has 200 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) = 1088

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)(19,22,23,24)(26,27,29,34,30,33,38,40,31,35,37,41,28,32,36,39);(18,19)(20,24)(21,23)(22,25)(27,32,35,33)(29,37)(34,39,41,40)(36,38)

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, 112);