C₁₇×#7262 #16865006

order	4352
nilpotency class	4
isoclinism	isoclinic class of #7262
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₇ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₇×#7262

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#340
commutator	C₂×C₈	C₄²×C₁₇
Frattini, cosocle	C₂³×C₈	C₂²×C₁₇
prime radical	C₂⁴×C₁₇	D₈
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ C₂³×C₈×C₁₇ ◁ G

352 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 106 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)(20,22)(21,24)(23,25)(27,32,33,40)(28,36)(29,30)(34,37,35,41)(38,39);(19,22,24,23)(26,27)(28,37)(29,35)(30,34)(31,33)(32,38)(36,40)(39,41)

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, 250);