C₁₇×#7525 #16865269

order	4352
nilpotency class	6
isoclinism	isoclinic class of #7523
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7525

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1404
commutator	#125	C₂×C₄×C₁₇
Frattini, cosocle	#491	C₂²×C₁₇
prime radical	C₁₇×#562	C₄
LCS	G ▷ #125 ▷ C₄² ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#491 ◁ G

138 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 30 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 2 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25,22,27,33,43)(20,28,30,41,29,39,46,48)(23,26,37,44,35,45,34,42)(24,32,38,36,40,47,49,31);(19,24)(20,29)(23,35)(25,41)(26,39)(27,40)(28,45)(32,47)(34,37)(38,44)(42,49)(43,48)

Conjugacy classes & character table

323 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 513);