C₁₇×#12924 #16870668

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

Aliases

direct product

C₁₇×#12924

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#447
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
socle	C₂×C₁₇	#1852
prime radical	C₂⁴×C₁₇	Q₁₆
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂²×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 386 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)(18,19,22,27,24,28,23,38)(20,29,32,46,31,45,39,43)(21,33,36,44,35,48,37,26)(25,34,41,47,40,49,42,30);(18,20,22,32,24,31,23,39)(19,25,27,41,28,40,38,42)(21,34,36,47,35,49,37,30)(26,43,33,29,44,46,48,45);(21,35)(26,44)(29,45)(30,47)(33,48)(34,49)(36,37)(43,46)

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, 5912);