C₁₃×#12845 #15699184

order	3328
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#12845

Subgroups

	subgroup	G/H
center	C₂²×C₈×C₁₃	C₂³
commutator	C₂³	C₂²×C₈×C₁₃
Frattini, cosocle	C₂²×C₈	C₂³×C₁₃
socle	C₂³×C₁₃	C₂²×C₈
prime radical	C₂⁴×C₁₃	C₂×C₈
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₈×C₁₃ ◁ G

454 conjugacy classes of subgroups; only the 182 normal subgroups are shown.

normal subgroups only

This group has 454 conjugacy classes of subgroups — too many to draw. Only its 182 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) = 57
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 57 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,17)(18,19)(20,23)(21,22)(24,25)(26,27,29,33,30,34,39,45,31,35,40,46,41,47,51,55)(28,32,37,43,38,44,50,54,36,42,48,52,49,53,56,57);(19,22)(23,25)(26,28)(27,32)(29,37)(30,38)(31,36)(33,43)(34,44)(35,42)(39,50)(40,48)(41,49)(45,54)(46,52)(47,53)(51,56)(55,57);(15,17)(18,20,21,24)(19,23,22,25)(28,36)(32,42)(37,48)(38,49)(43,52)(44,53)(50,56)(54,57)

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5833);