C₁₃×#13834 #15700173

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₁₃ · Schur multiplier (H₂) = C₂×C₄³

Aliases

direct product

C₁₃×#13834

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₁₃	C₂⁴
commutator	C₂²	C₂²×C₄²×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

1390 conjugacy classes of subgroups; only the 622 normal subgroups are shown.

normal subgroups only

This group has 1390 conjugacy classes of subgroups — too many to draw. Only its 622 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) = 3328

A minimal faithful permutation representation — 4 generators on 37 points:

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

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6822);