C₁₃×#7206 #15693545

order	3328
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₁₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₁₃×#7206

Subgroups

	subgroup	G/H
center	C₂×C₄×C₁₃	#99
commutator	C₂×C₄	C₄×C₈×C₁₃
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₃
socle	C₂²×C₁₃	#342
prime radical	C₂³×C₁₃	#95
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

284 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 102 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 — 2 generators on 37 points:

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

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, 194);