C₁₇×#23470 #16881214

order	4352
nilpotency class	3
isoclinism	isoclinic class of #23444
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₇ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₁₇×#23470

Subgroups

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

1178 conjugacy classes of subgroups; only the 334 normal subgroups are shown.

normal subgroups only

This group has 1178 conjugacy classes of subgroups — too many to draw. Only its 334 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 — 4 generators on 57 points:

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

Conjugacy classes & character table

782 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 16458);