C₁₇×#10428 #16868172

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10078
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#10428

Subgroups

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

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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) = 53
transitive degree	μ_t(G) = 4352

A minimal faithful permutation representation — 3 generators on 53 points:

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

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, 3416);