C₁₇×#7065 #16864809

order	4352
nilpotency class	4
isoclinism	isoclinic class of #1343
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7065

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#99
commutator	C₂²×C₄	C₂×C₈×C₁₇
Frattini, cosocle	C₂×C₄⋊C₈	C₂²×C₁₇
socle	C₂²×C₁₇	#324
prime radical	C₂³×C₁₇	C₂²⋊C₈
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₂×C₁₇×C₄⋊C₈ ◁ G

156 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 156 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 65
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 65 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,32)(21,29,30,24)(22,25)(23,27)(31,33)(34,35,37,42,38,43,48,56,39,41,47,53,49,54,60,63)(36,40,45,50,46,52,59,61,44,51,57,55,58,62,65,64);(18,20)(19,23,25,31)(21,27)(22,28)(24,26,29,32)(30,33)(34,36)(35,40,41,51)(37,45)(38,46)(39,44)(42,55,53,50)(43,52,54,62)(47,57)(48,59)(49,58)(56,64,63,61)(60,65)

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 53);