#13088293

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
LCS	G ▷ C₃×SL(2,𝔽₅)
UCS	C₁ ◁ C₂

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

normal subgroups only

This group has 144 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:

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

Conjugacy classes & character table

36 conjugacy classes — view the full character table.

Relationships

maximal subgroup of

#72277251

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4610);