C₁₃×#8755 #15695094

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8746
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#8755

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#381
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₂⁴×C₁₃	C₂²×C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

398 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 398 conjugacy classes of subgroups — too many to draw. Only its 110 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) = 832

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

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1743);