C₁₇×#12423 #16870167

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12416
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₇×#12423

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#459
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈²×C₁₇ ◁ G

218 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 82 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)(19,22)(20,24)(23,25)(26,27,29,32)(28,36,37,54)(30,42,40,55)(31,45,41,35)(33,49,47,38)(34,51,48,44)(39,56,46,52)(43,53,57,50);(18,19,20,22,21,23,24,25)(27,32)(33,47)(34,48)(35,45)(36,54)(42,55)(50,53)(52,56);(26,28,29,37)(27,33,32,47)(30,43,40,57)(31,46,41,39)(34,52,48,56)(35,53,45,50)(36,55,54,42)(38,51,49,44)

Conjugacy classes & character table

731 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5411);