C₁₃×#9070 #15695409

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#9070

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#120
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×C₄²	C₂³×C₁₃
socle	C₂²×C₁₃	#386
prime radical	C₁₃×#532	C₂²
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

426 conjugacy classes of subgroups; only the 126 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 126 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) = 1664

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

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

Conjugacy classes & character table

676 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 2058);