C₁₃×#11869 #15698208

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11867
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₁₃×#11869

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1519
commutator	C₂×C₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
prime radical	C₂×C₁₃×#41	D₄
LCS	G ▷ C₂×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#131 ◁ G

364 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 110 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)(16,27,30,58)(17,33)(18,39,42,56)(19,25)(20,45)(21,26)(22,29)(23,37)(24,43,54,44)(28,59,61,75)(31,52,32,66)(34,69,62,57)(35,53,41,50)(36,51)(38,68)(40,55)(46,70)(47,64)(48,65)(49,63)(60,76)(67,71,73,72)(74,77);(14,16,21,30)(15,22,26,48)(17,34,38,62)(18,40,42,64)(19,32,20,31)(23,49,51,76)(24,52,54,66)(25,55,45,47)(27,56,58,39)(28,37,61,36)(29,43,65,44)(33,46,68,74)(35,60,41,63)(50,57,53,69)(59,67,75,73)(70,71,77,72);(14,17,19,36,21,38,20,37)(15,23,45,68,26,51,25,33)(16,28,31,34,30,61,32,62)(18,41,43,72,42,35,44,71)(22,46,55,76,48,74,47,49)(24,53,56,67,54,50,39,73)(27,57,66,75,58,69,52,59)(29,63,64,77,65,60,40,70)

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, 4857);