C₁₃×#7448 #15693787

order	3328
nilpotency class	5
isoclinism	isoclinic class of #7447
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₁₃ · Schur multiplier (H₂) = C₂

Aliases

direct product

C₁₃×#7448

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1361
commutator	C₂×C₁₆	C₂×C₄×C₁₃
Frattini, cosocle	C₄×C₁₆	C₂²×C₁₃
prime radical	C₁₃×#2246	C₂
LCS	G ▷ C₂×C₁₆ ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₄×C₈×C₁₃ ◁ C₄×C₁₃×C₁₆ ◁ G

146 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 50 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 2 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,17,23,33,26,35,42,20,27,34,25,19,36,18,24)(16,28,30,22,41,40,45,39,32,43,44,38,31,21,29,37);(15,21)(16,29)(17,18)(19,33)(22,25)(23,38)(24,37)(26,43)(27,40)(28,36)(30,31)(32,45)(34,35)(39,42)(41,44)

Conjugacy classes & character table

481 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 436);