C₁₇×#8539 #16866283

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8534
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#8539

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₁₇×#3485	C₂
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

1008 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1008 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)(26,27,30,34,31,35,41,47)(28,32,38,44,37,43,51,55)(29,33,40,46,39,45,52,56)(36,48,50,57,49,42,53,54);(18,20)(19,22)(21,25)(23,24)(26,28)(27,32)(29,36)(30,38)(31,37)(33,42)(34,44)(35,43)(39,49)(40,50)(41,51)(45,48)(46,54)(47,55)(52,53)(56,57);(26,29)(27,33)(28,36)(30,40)(31,39)(32,42)(34,46)(35,45)(37,49)(38,50)(41,52)(43,48)(44,54)(47,56)(51,53)(55,57)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1527);