C₁₇×#12116 #16869860

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

Aliases

direct product

C₁₇×#12116

Subgroups

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

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

normal subgroups only

This group has 426 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)(20,29)(21,26)(22,34)(23,38)(24,28)(25,31)(27,36)(30,45)(32,46)(33,44)(35,40)(37,49)(39,43)(41,48)(42,47);(18,20)(19,25)(21,30)(22,35)(23,39)(24,32)(26,40)(27,43)(28,41)(29,34)(31,36)(33,48)(37,47)(38,42)(44,45)(46,49);(18,21,24,23)(19,26,28,38)(20,30,32,39)(22,36,37,33)(25,40,41,42)(27,34,44,49)(29,45,46,43)(31,47,48,35)

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, 5104);