#13088292

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

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

normal subgroups only

This group has 142 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:

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

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4609);