#13088291

order	1440
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₂	D₃×S₅
commutator, cosocle, hypocenter	C₃×SL(2,𝔽₅)	C₂²
Fitting, socle	C₂×C₃	C₂×S₅
prime radical	C₃⋊#6732	C₂
LCS	G ▷ C₃×SL(2,𝔽₅)
UCS	C₁ ◁ C₂

138 conjugacy classes of subgroups; only the 12 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 12 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 144

Permutation generators:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#72277416

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4608);