C₁₇×#19008 #16876752

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#19008

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₂³×C₁₇	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

786 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 786 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 2176

A minimal faithful permutation representation — 4 generators on 65 points:

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

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, 11996);