C₁₇×#62849 #16920593

order	4352
nilpotency class	2
isoclinism	isoclinic class of #62842
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₇ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₁₇×#62849

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂⁶
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₇
prime radical	C₂⁴×C₁₇	C₂⁴
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ G

6578 conjugacy classes of subgroups; only the 6270 normal subgroups are shown.

normal subgroups only

This group has 6578 conjugacy classes of subgroups — too many to draw. Only its 6270 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 — 6 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)(27,32)(30,42)(33,36)(34,43)(38,52)(41,53)(45,48)(51,57);(18,20,21,25)(19,22,23,24)(29,40)(34,43)(37,50)(41,53)(45,48)(47,54)(51,57)(55,56);(26,27,31,32)(28,36,39,33)(29,34,40,43)(30,35,42,44)(37,48,50,45)(38,49,52,46)(41,47,53,54)(51,56,57,55);(26,28,31,39)(27,33,32,36)(29,37,40,50)(30,38,42,52)(34,45,43,48)(35,46,44,49)(41,51,53,57)(47,55,54,56);(26,29)(27,34)(28,37)(30,41)(31,40)(32,43)(33,45)(35,47)(36,48)(38,51)(39,50)(42,53)(44,54)(46,55)(49,56)(52,57);(26,30)(27,35)(28,38)(29,41)(31,42)(32,44)(33,46)(34,47)(36,49)(37,51)(39,52)(40,53)(43,54)(45,55)(48,56)(50,57)

Conjugacy classes & character table

1394 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 55837);