C₁₇×#13715 #16871459

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

Aliases

direct product

C₁₇×#13715

Subgroups

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

176 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 74 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) = 2176

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

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, 6703);