C₁₇×#7339 #16865083

order	4352
nilpotency class	5
isoclinism	isoclinic class of #7339
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#7339

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1316
commutator	C₂²×C₄	C₂×C₈×C₁₇
Frattini, cosocle	#381	C₂²×C₁₇
prime radical	C₂²×#41×C₁₇	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂³ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂³×C₁₇ ◁ C₂⁴×C₁₇ ◁ C₁₇×#381 ◁ G

356 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 46 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 — 2 generators on 49 points:

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

Conjugacy classes & character table

476 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 327);