C₁₇×#12438 #16870182

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

Aliases

direct product

C₁₇×#12438

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₇	#1667
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#2213	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₇ ◁ C₂×C₄×C₁₇ ◁ C₄×C₈×C₁₇ ◁ G

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

normal subgroups only

This group has 224 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)(21,34)(22,35)(25,36)(27,41)(28,40)(30,31)(32,47)(33,42)(37,43)(38,39)(44,45)(48,49);(18,19,25,41,22,27,21,24,23,28,34,39,35,38,36,40)(20,26,42,48,31,44,30,37,33,46,29,43,32,45,47,49);(18,20)(19,26)(21,30)(22,31)(23,33)(24,37)(25,42)(27,44)(28,46)(29,34)(32,35)(36,47)(38,45)(39,43)(40,49)(41,48)

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, 5426);