#14515210

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂³ · Schur multiplier (H₂) = C₂²

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini, socle, cosocle	C₂²	C₂³×A₅
commutator	C₂×SL(2,𝔽₅)	C₂³
Fitting, hypercenter	C₄⋊Q₈	A₅
prime radical	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂×Q₈
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

472 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 45 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) = 192

Permutation generators:

(1,9,16,8,20,11,4,15,10,3,14,5)(2,17,23,12,13,24,7,22,21,6,19,18)(25,26)(27,28)(29,51,33,31,46,38,32,49,39,36,52,44)(30,41,42,34,45,43,35,47,48,40,50,37)(53,54)(55,56);(1,15,23,19,11,4,9,21,13,5)(2,7)(3,20,18,22,16,8,14,24,17,10)(6,12)(25,27,26,28)(29,30,47,48,52,32,35,41,42,46)(31,34,50,37,51,36,40,45,43,49)(33,39)(38,44)(53,56,54,55);(1,29,4,32)(2,30,7,35)(3,31,8,36)(5,33,11,39)(6,34,12,40)(9,37,15,43)(10,38,16,44)(13,41,19,47)(14,42,20,48)(17,45,22,50)(18,46,24,52)(21,49,23,51)(25,53,26,54)(27,55,28,56)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240908);