C₁₇×#8520 #16866264

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8516
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#8520

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₂²×#41×C₁₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

976 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 57
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 3 generators on 57 points:

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

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, 1508);