C₁₇×#12876 #16870620

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12876

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#481
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#1824
prime radical	C₂⁴×C₁₇	Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 138 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)(18,19,22,27,24,28,23,39)(20,29,32,43,30,45,33,48)(21,34,37,42,35,49,38,26)(25,36,41,31,40,47,44,46);(21,35)(26,42)(29,45)(31,46)(34,49)(36,47)(37,38)(43,48);(18,20,23,32,24,30,22,33)(19,25,27,44,28,40,39,41)(21,36,38,31,35,47,37,46)(26,43,34,29,42,48,49,45)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5864);