#14514726

order	1920
automorphism	?
homology	Abelianization (H₁) = C₄² · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×A₅	C₄²
Fitting, hypercenter	C₄²	S₅
socle, prime radical	C₂²×A₅	C₂×C₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#97
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂×C₄ ◁ C₄²

319 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 319 conjugacy classes of subgroups — too many to draw. Only its 29 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) = 160

Permutation generators:

(1,2,4,3)(6,33,13,34,7,32,12,35)(8,31,11,36,9,30,10,37)(14,22,21,29,15,23,20,28)(16,24,19,27,17,25,18,26);(3,5,4)(6,19,9,20)(7,18,8,21)(10,14,13,17)(11,15,12,16)(22,35,25,36)(23,34,24,37)(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, 240424);