C₁₃×#13053 #15699392

order	3328
nilpotency class	4
isoclinism	isoclinic class of #2202
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13053

Subgroups

	subgroup	G/H
center	C₄×C₁₃	B(4,𝔽₂)
commutator	C₂×Q₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×#41	C₂³×C₁₃
socle	C₂×C₁₃	#1889
prime radical	C₁₃×#3018	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

624 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 624 conjugacy classes of subgroups — too many to draw. Only its 114 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,19,24)(16,25)(17,22,26,35)(18,23)(20,30)(21,33)(27,38)(28,43,32,42)(29,40)(31,39)(34,41)(36,45,37,44);(14,16,26,27,19,29,17,30)(15,20,35,25,24,38,22,40)(18,32,34,45,33,28,31,44)(21,36,39,42,23,37,41,43);(15,21)(18,33)(20,36)(22,41)(23,24)(25,42)(28,32)(31,34)(35,39)(37,38)(40,43)(44,45)

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6041);