#13088289

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:

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

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, 4606);