C₁₇×#12061 #16869805

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12061

Subgroups

	subgroup	G/H
center	C₂×C₈×C₁₇	C₂×D₄
commutator	C₂×C₄	C₂²×C₈×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
socle, prime radical	C₂²×C₁₇	C₈×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

200 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 4352

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

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5049);