C₁₃×#7238 #15693577

order	3328
nilpotency class	4
isoclinism	isoclinic class of #7213
automorphism	?
homology	Abelianization (H₁) = C₄²×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#7238

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	#342
commutator	C₂²×C₄	C₄²×C₁₃
Frattini, cosocle	C₂×C₄×Q₈	C₂²×C₁₃
prime radical	C₂³×C₁₃	#95
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ C₂×C₄×Q₈×C₁₃ ◁ G

280 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 94 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) = 37
transitive degree	μ_t(G) = 1664

A minimal faithful permutation representation — 2 generators on 37 points:

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

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, 226);