C₁₇×#12109 #16869853

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12108
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12109

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₁₇
prime radical	C₁₇×#2018	C₂
LCS	G ▷ C₂²×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂²×C₄×C₁₇ ◁ C₁₇×#408 ◁ G

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

normal subgroups only

This group has 410 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) = 1088

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5097);