C₁₃×#11522 #15697861

order	3328
nilpotency class	4
isoclinism	isoclinic class of #11522
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₁₃×#11522

Subgroups

	subgroup	G/H
center	C₄×C₁₃	#410
commutator	C₂²×C₄	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×M₁₆	C₂³×C₁₃
socle	C₂×C₁₃	#1464
prime radical	C₂⁴×C₁₃	M₁₆
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₃ ◁ C₄²×C₁₃ ◁ C₄×C₁₃×M₁₆ ◁ G

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

normal subgroups only

This group has 284 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) = 45
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 3 generators on 45 points:

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

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, 4510);