C₁₃×#13359 #15699698

order	3328
nilpotency class	4
isoclinism	isoclinic class of #13357
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#13359

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	B(4,𝔽₂)
commutator, Frattini, cosocle	C₂²×Q₈	C₂³×C₁₃
prime radical	C₂×C₁₃×2₋¹⁺⁴	C₂²
LCS	G ▷ C₂²×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₁₃ ◁ C₂²×Q₈×C₁₃ ◁ G

704 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 98 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) = 832

A minimal faithful permutation representation — 3 generators on 33 points:

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

Conjugacy classes & character table

403 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6347);