C₁₃×#7387 #15693726

order	3328
nilpotency class	5
isoclinism	isoclinic class of D₃₂
automorphism	?
homology	Abelianization (H₁) = C₂×C₈×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#7387

Subgroups

	subgroup	G/H
center	C₈×C₁₃	D₁₆
commutator	C₁₆	C₂×C₈×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
socle	C₂×C₁₃	#1331
prime radical	C₁₃×#508	C₄
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₁₃ ◁ C₂×C₈×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

120 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 54 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)(14,15,18,24,20,25,40,53,21,27,41,54,44,26,19,42)(16,28,30,56,31,57,62,76,33,58,63,77,32,64,43,49)(17,34,36,50,38,65,71,52,39,67,72,51,73,66,37,23)(22,35,45,59,47,68,74,61,48,70,75,60,55,69,46,29);(14,16)(15,22)(17,35)(18,30)(19,43)(20,31)(21,33)(23,49)(24,45)(25,47)(26,55)(27,48)(28,34)(29,37)(32,44)(36,59)(38,68)(39,70)(40,62)(41,63)(42,46)(50,56)(51,77)(52,76)(53,74)(54,75)(57,65)(58,67)(60,72)(61,71)(64,66)(69,73)

Conjugacy classes & character table

988 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 375);