C₁₇×#12436 #16870180

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12436
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12436

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 234 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) = 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)(19,24)(20,29)(21,25)(22,34)(27,45)(28,39)(30,31)(32,46)(33,47)(35,40)(36,41)(37,38)(42,43)(48,49);(18,19,25,38,22,27,35,39,23,28,40,45,34,37,21,24)(20,26,29,41,31,42,46,49,33,44,47,48,32,43,30,36);(18,20)(19,26)(21,30)(22,31)(23,33)(24,36)(25,29)(27,42)(28,44)(32,34)(35,46)(37,43)(38,41)(39,49)(40,47)(45,48)

Conjugacy classes & character table

629 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5424);