C₁₇×#7410 #16865154

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7410
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7410

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1344
commutator	C₂²×C₈	C₂×C₄×C₁₇
Frattini, cosocle	#408	C₂²×C₁₇
prime radical	C₂×#41×C₁₇	D₄
LCS	G ▷ C₂²×C₈ ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#408 ◁ G

166 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 166 conjugacy classes of subgroups — too many to draw. Only its 42 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)(18,19,21,26)(20,25,30,39)(22,28,34,42)(23,27,33,43)(24,36,37,46)(29,38,45,49)(31,40,47,41)(32,48,35,44);(19,24,28,38)(20,29)(21,32)(23,35)(25,27,40,44)(26,39,42,41)(31,46)(33,34)(36,45)(37,48,49,43)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 398);