C₁₃×#8540 #15694879

order	3328
nilpotency class	3
isoclinism	isoclinic class of #8534
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#8540

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#379
commutator	C₂⁴	C₂²×C₄×C₁₃
Frattini, cosocle	C₂³×C₄	C₂³×C₁₃
prime radical	C₁₃×#534	C₄
LCS	G ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

718 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 718 conjugacy classes of subgroups — too many to draw. Only its 142 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) = 61
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 61 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15)(16,22,24,19)(17,20)(18,21)(23,28,29,26)(25,27)(30,31,34,38,35,39,45,51)(32,36,42,48,41,47,55,59)(33,37,44,50,43,49,56,60)(40,52,54,61,53,46,57,58);(14,16)(15,19)(17,23)(18,24)(20,26)(21,22)(25,29)(27,28)(30,32)(31,36)(33,40)(34,42)(35,41)(37,46)(38,48)(39,47)(43,53)(44,54)(45,55)(49,52)(50,58)(51,59)(56,57)(60,61);(14,17,18,25)(15,20,21,27)(16,23,24,29)(19,26,22,28)(30,33)(31,37)(32,40)(34,44)(35,43)(36,46)(38,50)(39,49)(41,53)(42,54)(45,56)(47,52)(48,58)(51,60)(55,57)(59,61)

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 1528);