C₁₇×#12362 #16870106

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

Aliases

direct product

C₁₇×#12362

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂×D₈×C₁₇	D₄
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ C₁₇×#446 ◁ G

292 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 57
transitive degree	μ_t(G) = 2176

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,24)(21,25)(26,27,32,36)(28,37,40,55)(29,34,31,46)(30,42,45,53)(33,48,50,39)(35,41,54,44)(38,56,47,52)(43,49,57,51);(18,19,22,20)(21,24,25,23)(26,28,32,40)(27,33,36,50)(29,38,31,47)(30,43,45,57)(34,49,46,51)(35,52,54,56)(37,53,55,42)(39,41,48,44);(18,20,22,19)(21,23,25,24)(26,29,32,31)(27,34,36,46)(28,38,40,47)(30,44,45,41)(33,49,50,51)(35,53,54,42)(37,52,55,56)(39,57,48,43)

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, 5350);