C₁₇×#11391 #16869135

order	4352
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#11391

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₇	#120
commutator	C₂⁴	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
socle	C₂²×C₁₇	#379
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

842 conjugacy classes of subgroups; only the 254 normal subgroups are shown.

normal subgroups only

This group has 842 conjugacy classes of subgroups — too many to draw. Only its 254 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) = 1088

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)(26,27,30,35,31,34,43,48)(28,36,39,49,38,32,42,45)(29,33,41,46,40,47,53,57)(37,44,52,55,51,50,54,56);(18,19,21,23)(20,24,25,22)(26,28)(27,32)(29,37)(30,42)(31,38)(33,44)(34,36)(35,49)(39,43)(40,51)(41,54)(45,48)(46,56)(47,50)(52,53)(55,57);(18,20,21,25)(19,22,23,24)(26,29)(27,33)(28,37)(30,41)(31,40)(32,44)(34,47)(35,46)(36,50)(38,51)(39,52)(42,54)(43,53)(45,55)(48,57)(49,56)

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, 4379);