C₁₇×#23840 #16881584

order	4352
nilpotency class	3
isoclinism	isoclinic class of #23391
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₇×#23840

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₄³×C₁₇ ◁ G

662 conjugacy classes of subgroups; only the 270 normal subgroups are shown.

normal subgroups only

This group has 662 conjugacy classes of subgroups — too many to draw. Only its 270 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) = 4352

A minimal faithful permutation representation — 4 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)(20,24,21,23)(26,27,30,33)(28,32,29,31)(34,35,38,41)(36,39,43,47)(37,40,45,49)(42,46,44,48);(18,20,22,21)(19,23,25,24)(26,28,30,29)(27,31,33,32)(34,36)(35,39)(37,42)(38,43)(40,46)(41,47)(44,45)(48,49);(18,20,22,21)(19,24,25,23)(26,29,30,28)(27,32,33,31)(36,42)(37,45)(39,46)(40,49)(43,44)(47,48);(18,21,22,20)(19,23,25,24)(36,43)(39,47)(42,44)(46,48)

Conjugacy classes & character table

884 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 16828);