C₁₇×#7055 #16864799

order	4352
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂×C₁₆×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#7055

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂³	C₂×C₁₆×C₁₇
Frattini, cosocle	C₂×C₂²⋊C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#323
prime radical	C₂⁴×C₁₇	C₂×C₈
LCS	G ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₂²⋊C₈ ◁ G

240 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 62 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) = 1088

A minimal faithful permutation representation — 2 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)(21,29,30,24)(22,25)(23,27,31,33)(28,32)(34,35,36,39,37,40,42,45,38,41,43,46,44,47,48,49);(18,20,22,28)(19,23,25,31)(21,27,30,33)(24,26,29,32)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 43);