C₁₇×#12309 #16870053

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12307
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12309

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1616
commutator, Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
prime radical	C₁₇×#469	C₂²
LCS	G ▷ C₂×M₁₆ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₂×M₁₆×C₁₇ ◁ G

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

normal subgroups only

This group has 280 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)(18,19,24,28,23,29,22,26)(20,30,32,47,34,48,33,44)(21,35,38,45,37,43,39,27)(25,40,41,31,42,36,46,49);(18,20)(19,25)(21,36)(22,32)(23,34)(24,33)(26,41)(27,44)(28,46)(29,42)(30,43)(31,38)(35,48)(37,40)(39,49)(45,47);(19,26,29,28)(21,37)(25,41,42,46)(27,43,45,35)(30,47,48,44)(31,49)(36,40)(38,39)

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, 5297);