C₁₇×#12115 #16869859

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12114
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#12115

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1595
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₁₇×#2010	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×M₁₆×C₁₇ ◁ G

422 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 49
transitive degree	μ_t(G) = 544

A minimal faithful permutation representation — 3 generators on 49 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,32)(22,37)(23,27)(24,29)(25,36)(26,35)(30,48)(31,45)(33,43)(34,44)(38,41)(39,47)(40,49)(42,46);(18,20,23,31)(19,24,27,39)(21,33,34,49)(22,38,35,30)(25,41,42,48)(26,43,37,40)(28,44,45,32)(29,46,47,36);(21,34)(29,47)(33,49)(36,46)

Conjugacy classes & character table

425 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5103);