C₁₇×#10225 #16867969

order	4352
nilpotency class	3
isoclinism	isoclinic class of #10218
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₇ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₇×#10225

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	#392
commutator, Frattini, cosocle	C₂×C₄²	C₂³×C₁₇
prime radical	C₁₇×#3150	C₂
LCS	G ▷ C₂×C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

574 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 574 conjugacy classes of subgroups — too many to draw. Only its 122 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)(20,23)(21,24)(22,25)(26,27,32,37)(28,38,41,49)(29,34,45,52)(30,36,31,35)(33,42,48,40)(39,54,55,50)(43,57,56,47)(44,53,46,51);(19,23)(20,21)(24,25)(26,28)(27,33)(29,43)(30,42)(31,40)(32,41)(34,50)(35,49)(36,38)(37,48)(39,44)(45,56)(46,55)(47,51)(52,54)(53,57);(19,24)(20,21)(23,25)(26,29)(27,34)(28,39)(30,44)(31,46)(32,45)(33,47)(35,51)(36,53)(37,52)(38,50)(40,43)(41,55)(42,56)(48,57)(49,54)

Conjugacy classes & character table

578 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 3213);