C₁₇×#8464 #16866208

order	4352
nilpotency class	3
isoclinism	isoclinic class of #8453
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₇ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₇×#8464

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#379
commutator	C₂²×C₄	C₂²×C₄×C₁₇
Frattini, cosocle	C₂³×C₄	C₂³×C₁₇
prime radical	C₁₇×#3487	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂³×C₄×C₁₇ ◁ G

1002 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 1002 conjugacy classes of subgroups — too many to draw. Only its 150 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)(18,19)(20,24,25,22)(21,23)(26,27,31,36,32,37,30,35)(28,38,42,33,41,48,40,47)(29,34,43,49,44,50,45,51)(39,53,54,57,55,52,56,46);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,39)(30,42)(31,40)(32,41)(34,46)(35,48)(36,38)(37,47)(43,56)(44,55)(45,54)(49,52)(50,57)(51,53);(26,29,32,44)(27,34,37,50)(28,39,41,55)(30,45,31,43)(33,46,47,57)(35,51,36,49)(38,52,48,53)(40,56,42,54)

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, 1452);