C₂³×C₁₃×#125 #15749000

order	3328
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁶×C₁₃ · Schur multiplier (H₂) = C₂¹³

Aliases

direct product

C₂³×C₁₃×#125

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁵×C₁₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵×C₁₃ ◁ G

8414 conjugacy classes of subgroups; only the 6878 normal subgroups are shown.

normal subgroups only

This group has 8414 conjugacy classes of subgroups — too many to draw. Only its 6878 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) = 35
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 6 generators on 35 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35);(3,4);(5,6);(9,13)(11,14)(15,16,18,20)(17,19,21,22);(7,8,10,12)(9,11,13,14)(15,16)(17,19)(18,20)(21,22);(7,9)(8,11)(10,13)(12,14)(15,17,18,21)(16,19,20,22)

Conjugacy classes & character table

1456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 55649);