C₁₃×#12397 #15698736

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12316
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#12397

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#447
commutator, Frattini, cosocle	C₄×C₈	C₂³×C₁₃
prime radical	C₂×D₄×C₁₃	D₈
LCS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₄²×C₁₃ ◁ C₈×D₄×C₁₃ ◁ G

278 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 82 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) = 61
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 3 generators on 61 points:

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

Conjugacy classes & character table

520 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5385);