C₁₃×#19067 #15705406

order	3328
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#19067

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂³×C₁₃	#120
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

784 conjugacy classes of subgroups; only the 222 normal subgroups are shown.

normal subgroups only

This group has 784 conjugacy classes of subgroups — too many to draw. Only its 222 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) = 1664

A minimal faithful permutation representation — 4 generators on 61 points:

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

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, 12055);