C₁₇×#19058 #16876802

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

Aliases

direct product

C₁₇×#19058

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

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

normal subgroups only

This group has 840 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)(18,19,22,25)(20,26,27,33)(21,29,30,24)(23,31,32,28)(34,35)(36,46)(37,51)(38,43)(39,44)(40,45)(41,49)(42,53)(47,55)(48,56)(50,59)(52,57)(54,58)(60,62)(61,64)(63,65);(21,30)(24,29)(26,33)(28,31)(34,36)(35,41)(37,47)(38,48)(39,49)(40,50)(42,55)(43,46)(44,59)(45,56)(51,64)(52,61)(53,62)(54,63)(57,65)(58,60);(18,20)(19,23)(21,31)(22,27)(24,33)(25,32)(26,29)(28,30)(34,37,40,54)(35,42,45,57)(36,47,50,63)(38,53,39,52)(41,55,56,65)(43,58,44,51)(46,60,59,64)(48,62,49,61);(34,38,40,39)(35,43,45,44)(36,48,50,49)(37,52,54,53)(41,46,56,59)(42,51,57,58)(47,61,63,62)(55,64,65,60)

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, 12046);