C₁₃×#12471 #15698810

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12433
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₃×#12471

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#466
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₁₃×#1667	C₂
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 78 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) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,18)(17,19)(20,21)(23,27)(24,28)(25,31)(29,33)(30,37)(32,36)(34,35);(15,18)(19,20)(22,23,28,35,25,30,32,33,26,29,36,37,31,34,24,27);(15,19)(17,21)(18,20)(23,29)(27,33)(30,34)(35,37)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5459);