C₁₃×#13647 #15699986

order	3328
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃×C₁₆ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#13647

Subgroups

	subgroup	G/H
center	C₁₃×C₃₂	D₄
commutator	C₄	C₂²×C₁₃×C₁₆
Frattini, cosocle	C₂×C₁₆	C₂³×C₁₃
socle	C₂×C₁₃	D₄×C₁₆
prime radical	C₁₃×#135	C₈
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₁₃×C₃₂ ◁ C₂×C₁₃×C₃₂ ◁ G

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

normal subgroups only

This group has 186 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) = 77
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 3 generators on 77 points:

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

Conjugacy classes & character table

1456 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 6635);