C₁₃×#32704 #15719043

order	3328
nilpotency class	3
isoclinism	isoclinic class of #31076
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂²×C₄

Aliases

direct product

C₁₃×#32704

Subgroups

	subgroup	G/H
center	C₄×C₁₃	H(3,𝔽₄)
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₃
socle	C₂×C₁₃	#2804
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

556 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 194 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) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 25692);