#14514805

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄ · Schur multiplier (H₂) = C₂³

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, Frattini	C₂²	C₂²×S₅
commutator	C₂×A₅	C₂²×C₄
Fitting, hypercenter	C₄⋊C₄	S₅
socle, prime radical, cosocle	C₂²×A₅	C₂³
hypocenter	A₅	C₄×Q₈
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₄⋊C₄

565 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 565 conjugacy classes of subgroups — too many to draw. Only its 43 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) = 96

Permutation generators:

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

Conjugacy classes & character table

70 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240503);