C₁₇×#13076 #16870820

order	4352
nilpotency class	4
isoclinism	isoclinic class of #13074
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#13076

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1893
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#3060	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

466 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 146 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 — 3 generators on 49 points:

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

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, 6064);