#14514769

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₈ · Schur multiplier (H₂) = C₂

non-solvable

Aliases

No aliases for this group.

Splittings

Fitting

C₁₆ ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₈	C₂×S₅
commutator, socle	C₂×A₅	C₂×C₈
Fitting, hypercenter	C₁₆	S₅
prime radical	C₂×S₅	C₈
cosocle	C₈×A₅	C₂²
hypocenter	A₅	M₃₂
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₈ ◁ C₁₆

167 conjugacy classes of subgroups; only the 17 normal subgroups are shown.

normal subgroups only

This group has 167 conjugacy classes of subgroups — too many to draw. Only its 17 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) = 80

Permutation generators:

(1,5,2,3)(6,19,8,21,7,18,9,20)(10,17,12,14,11,16,13,15)(22,35,24,37,23,34,25,36)(26,33,28,30,27,32,29,31);(2,4)(3,5)(6,34,13,30,9,37,11,33,7,35,12,31,8,36,10,32)(14,27,21,23,17,28,19,24,15,26,20,22,16,29,18,25)

Conjugacy classes & character table

76 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240467);