C₁₃×#13749 #15700088

order	3328
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₄³×C₁₃ · Schur multiplier (H₂) = C₂²×C₄³

Aliases

direct product

C₁₃×#13749

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂	C₂×C₄³×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁵×C₁₃	C₂³
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

2598 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.

normal subgroups only

This group has 2598 conjugacy classes of subgroups — too many to draw. Only its 1374 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) = 33
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 4 generators on 33 points:

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

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6737);