C₁₇×#11537 #16869281

order	4352
nilpotency class	4
isoclinism	isoclinic class of #11521
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₇×#11537

Subgroups

	subgroup	G/H
center	C₄×C₁₇	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₇
socle	C₂×C₁₇	#1466
prime radical	C₁₇×#525	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₇ ◁ C₂×C₈×C₁₇ ◁ C₁₇×#405 ◁ G

348 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 348 conjugacy classes of subgroups — too many to draw. Only its 102 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)(18,19,21,26,22,27,34,42,23,24,33,37,35,38,45,49)(20,28,29,44,30,36,46,41,31,43,32,48,47,25,39,40);(19,24)(25,36)(27,38)(28,43);(18,20,22,30,23,31,35,47)(19,25,38,43,24,36,27,28)(21,32,34,39,33,29,45,46)(26,41,49,44,37,40,42,48)

Conjugacy classes & character table

680 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 4525);