C₁₃×#12692 #15699031

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11502
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#12692

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#99
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂²×D₄	C₂³×C₁₃
prime radical	C₂²×C₁₃×#41	C₂²
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂²×C₁₃×#41 ◁ G

976 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 976 conjugacy classes of subgroups — too many to draw. Only its 150 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) = 49
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 49 points:

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

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, 5680);