C₁₃×#11990 #15698329

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11989
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11990

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1551
commutator	C₄²	C₂²×C₄×C₁₃
Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₂³×C₁₃	#100
LCS	G ▷ C₄² ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₁₃×#405 ◁ G

268 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 268 conjugacy classes of subgroups — too many to draw. Only its 98 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)(14,15,18,24,19,23,37,49,20,26,38,52,40,25,53,51)(16,27,29,55,30,44,59,69,31,43,60,50,39,21,36,42)(17,32,34,61,35,22,45,46,33,48,62,74,63,47,71,73)(28,41,57,67,58,54,75,76,56,68,70,77,65,66,64,72);(14,16,20,31)(15,21,26,44)(17,28,33,56)(18,36,38,59)(19,39,40,30)(22,41,47,68)(23,43,25,27)(24,50,52,55)(29,37,60,53)(32,54,48,66)(34,64,62,75)(35,65,63,58)(42,49,69,51)(45,70,71,57)(46,72,73,76)(61,67,74,77);(14,17)(15,22,26,47)(16,28)(18,34)(19,35)(20,33)(21,41,44,68)(23,48,25,32)(24,46,52,73)(27,54,43,66)(29,57)(30,58)(31,56)(36,64)(37,45)(38,62)(39,65)(40,63)(42,67,69,77)(49,74,51,61)(50,72,55,76)(53,71)(59,75)(60,70)

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, 4978);