C₁₃×#11653 #15697992

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11651
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11653

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×#102
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#102
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂×C₄²×C₁₃ ◁ C₂×C₄×C₈×C₁₃ ◁ G

300 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 118 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 — 3 generators on 61 points:

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

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 4641);