C₂×C₅₃×#1713 #27227114

order	13568
nilpotency class	3
isoclinism	isoclinic class of #1705
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₅₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂×C₅₃×#1713

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₅₃	#127
commutator, Frattini, cosocle	C₄²	C₂⁴×C₅₃
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₅₃ ◁ C₂×C₄²×C₅₃ ◁ G

878 conjugacy classes of subgroups; only the 382 normal subgroups are shown.

normal subgroups only

This group has 878 conjugacy classes of subgroups — too many to draw. Only its 382 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) = 79
transitive degree	μ_t(G) = 13568

A minimal faithful permutation representation — 4 generators on 79 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53)(54,55);(57,60)(58,61)(62,63)(64,65,68,71)(66,72,75,79)(67,76,73,70)(69,77,78,74);(64,66,73,77,68,75,67,74)(65,69,76,79,71,78,70,72);(56,57,61,63,59,62,58,60)

Conjugacy classes & character table

4028 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 12590);