#14514732

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂³

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂	C₂²⋊(A₅⋊C₄)
commutator	C₂²×A₅	C₂×C₄
Frattini	C₂³	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
socle	C₂×A₅	C₂²⋊C₄
prime radical	C₂×D₄×A₅	C₂
cosocle	C₂³×A₅	C₂²
hypocenter	A₅	#99
LCS	G ▷ C₂²×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ C₂³ ◁ C₂×D₄

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

normal subgroups only

This group has 493 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) = 40

Permutation generators:

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

Conjugacy classes & character table

43 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240430);