C₁₃×#7449 #15693788

order	3328
nilpotency class	5
isoclinism	isoclinic class of #7447
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#7449

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
prime radical	C₂²×C₁₃	#361
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

126 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 2 generators on 77 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,18,24,41,27,43,53,21,28,42,26,20,44,19,25)(16,29,31,60,45,62,69,77,34,63,68,52,33,70,32,61)(17,35,37,23,51,54,64,56,40,72,75,57,39,55,38,71)(22,36,46,30,49,65,58,76,50,74,48,67,59,73,47,66);(14,16,21,34)(15,22,28,50)(17,36,40,74)(18,32,42,69)(19,31,43,68)(20,45,41,33)(23,52,57,60)(24,47,26,58)(25,46,53,48)(27,59,44,49)(29,54,63,55)(30,64,67,38)(35,70,72,62)(37,66,75,76)(39,65,51,73)(56,77,71,61)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 437);