C₁₇×#12021 #16869765

order	4352
nilpotency class	4
isoclinism	isoclinic class of #12019
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₇×#12021

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#106
commutator	C₂×C₈	C₂²×C₄×C₁₇
Frattini, cosocle	C₄×C₈	C₂³×C₁₇
prime radical	C₂³×C₁₇	#106
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ C₂×C₄×C₈×C₁₇ ◁ G

216 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 126 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)(18,19,20,23,21,22,24,25)(26,27)(28,37,40,52)(29,34)(30,43)(31,46)(32,36)(33,39,48,55)(35,44)(38,51,41,53)(42,50)(45,57)(47,54,49,56);(26,28,30,39,31,38,44,54,32,40,45,55,29,41,42,56)(27,33,35,37,34,49,43,53,36,48,50,52,46,47,57,51);(19,22)(23,25)(26,29,32,31)(27,34,36,46)(28,38,40,41)(30,42,45,44)(33,47,48,49)(35,43,50,57)(37,51,52,53)(39,54,55,56)

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, 5009);