C₁₇×#12301 #16870045

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12301
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12301

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1613
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₁₇×#3199	C₂
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 342 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)(18,19,22,38,23,28,39,27)(20,29,32,44,33,43,31,25)(21,34,36,26,37,24,35,41)(30,42,48,46,49,45,47,40);(19,24)(21,35)(22,39)(25,40)(26,38)(27,41)(28,34)(29,45)(30,47)(31,32)(36,37)(42,43)(44,46)(48,49);(18,20)(19,25)(21,30)(22,32)(23,33)(24,40)(26,45)(27,43)(28,44)(29,38)(31,39)(34,46)(35,47)(36,48)(37,49)(41,42)

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, 5289);