#14514768

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

non-solvable

Aliases

No aliases for this group.

Subgroups

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

197 conjugacy classes of subgroups; only the 21 normal subgroups are shown.

normal subgroups only

This group has 197 conjugacy classes of subgroups — too many to draw. Only its 21 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:

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

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, 240466);