C₁₇×#12046 #16869790

order	4352
nilpotency class	4
isoclinism	isoclinic class of D₁₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12046

Subgroups

	subgroup	G/H
center	C₁₆×C₁₇	D₈
commutator	C₈	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle	C₂×C₁₇	C₈×D₈
prime radical	C₁₇×#508	C₄
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₆×C₁₇ ◁ C₂×C₁₆×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

216 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 106 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)(18,19,23,29,25,30,41,28,26,31,22,40,24,20,32,34)(21,27,36,43,38,44,49,42,39,45,35,48,37,33,46,47);(18,20)(19,25)(21,33)(22,28)(23,34)(24,31)(26,30)(27,38)(29,41)(32,40)(35,42)(36,47)(37,45)(39,44)(43,49)(46,48);(18,21,23,36,25,38,41,49,26,39,22,35,24,37,32,46)(19,27,29,43,30,44,28,42,31,45,40,48,20,33,34,47)

Conjugacy classes & character table

1496 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5034);