C₁₇×#7388 #16865132

order	4352
nilpotency class	5
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#7388

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#357
commutator	C₁₆	C₂×C₈×C₁₇
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₇
socle	C₂×C₁₇	#1331
prime radical	C₁₇×#508	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

118 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 118 conjugacy classes of subgroups — too many to draw. Only its 54 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) = 81
transitive degree	μ_t(G) = 1088

A minimal faithful permutation representation — 2 generators on 81 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,28,24,29,46,56,25,31,41,61,49,30,23,47)(20,32,34,64,36,66,48,65,38,67,35,73,37,74,69,55)(21,39,42,57,44,75,68,59,45,63,79,58,80,76,43,27)(26,50,51,71,53,78,52,33,54,40,60,70,62,77,81,72);(18,20)(19,26)(21,40)(22,35)(23,48)(24,36)(25,38)(27,55)(28,60)(29,53)(30,62)(31,54)(32,63)(33,68)(34,41)(37,49)(39,67)(42,71)(43,72)(44,77)(45,50)(46,69)(47,52)(51,61)(56,81)(57,64)(58,73)(59,65)(66,76)(70,79)(74,75)(78,80)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 376);