C₁₇×#7078 #16864822

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7076
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7078

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#327
commutator	C₂²×C₈	C₂×C₄×C₁₇
Frattini, cosocle	C₂×C₂²⋊C₈	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	D₈
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₂²⋊C₈ ◁ G

286 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 54 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)(18,19)(20,24,25,22)(21,23)(27,31)(28,34)(29,36)(32,41)(33,40)(35,38)(37,39);(19,22)(23,24)(26,27,30,33)(28,35,37,41)(29,38,36,32)(31,39,40,34)

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, 66);