C₁₇×#12390 #16870134

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12324
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#12390

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₁₇×#3403	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#446 ◁ G

302 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 2176

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

Conjugacy classes & character table

527 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 5378);