C₁₇×#13706 #16871450

order	4352
nilpotency class	5
isoclinism	isoclinic class of #13661
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#13706

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	C₂×D₁₆
commutator, Frattini, cosocle	C₂×C₁₆	C₂³×C₁₇
LCS	G ▷ C₂×C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₄×C₈×C₁₇ ◁ C₄×C₁₆×C₁₇ ◁ G

164 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 4352

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

Conjugacy classes & character table

833 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 6694);