C₁₃×#15190 #15701529

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product

C₁₃×#15190

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

2278 conjugacy classes of subgroups; only the 590 normal subgroups are shown.

normal subgroups only

This group has 2278 conjugacy classes of subgroups — too many to draw. Only its 590 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) = 33
transitive degree	μ_t(G) = 3328

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

832 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 8178);