C₁₇×#12810 #16870554

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11522
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12810

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×#41	C₂³×C₁₇
socle	C₂×C₁₇	#1799
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₂×C₁₇×#131 ◁ G

412 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 412 conjugacy classes of subgroups — too many to draw. Only its 126 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)(18,19,23,27,24,29,21,35)(20,30,34,40,31,45,32,25)(22,28,36,42,37,26,38,43)(33,44,47,39,46,49,48,41);(18,20,21,32,24,31,23,34)(19,25,27,30,29,40,35,45)(22,33,36,47,37,46,38,48)(26,41,42,49,28,39,43,44);(19,26)(20,31)(22,37)(25,39)(27,42)(28,29)(30,44)(32,34)(35,43)(36,38)(40,41)(45,49)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5798);