C₁₃×#18999 #15705338

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

Aliases

direct product

C₁₃×#18999

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ G

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

normal subgroups only

This group has 850 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) = 832

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

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

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, 11987);