C₁₇×#12405 #16870149

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12405

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₈×Q₈×C₁₇ ◁ G

276 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 86 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) = 4352

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

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5393);