C₅₃×#13448 #27220960

order	13568
nilpotency class	4
isoclinism	isoclinic class of #13304
automorphism	?
homology	Abelianization (H₁) = C₂³×C₅₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₅₃×#13448

Subgroups

	subgroup	G/H
center, socle	C₂³×C₅₃	C₂×D₈
commutator, Frattini, cosocle	C₂²×C₈	C₂³×C₅₃
prime radical	C₂²×D₁₆×C₅₃	C₂
LCS	G ▷ C₂²×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ C₂×C₄×C₈×C₅₃ ◁ G

482 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 482 conjugacy classes of subgroups — too many to draw. Only its 130 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) = 77
transitive degree	μ_t(G) = 6784

A minimal faithful permutation representation — 3 generators on 77 points:

(1,2)(3,4)(10,17)(11,19)(12,14)(13,21)(15,23)(18,22)(20,24)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77);(5,6)(7,8)(9,10)(11,21)(12,18)(13,24)(14,17)(15,22)(16,20)(19,23);(2,4)(6,8)(9,11,12,20,23,24,13,19,16,18,21,10,15,17,14,22)

Conjugacy classes & character table

2756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 6436);