#14514745

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₂²

non-solvable

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center	C₂²	C₂²⋊S₅
commutator	C₄×A₅	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×Q₈	S₅
socle, prime radical	C₂²×A₅	D₄
cosocle	C₂×C₄×A₅	C₂²
hypocenter	A₅	#103
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×Q₈

371 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 371 conjugacy classes of subgroups — too many to draw. Only its 25 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:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	#72276835, SD₁₆×A₅⋊C₄
maximal normal subgroup of	SD₁₆×A₅⋊C₄
maximal quotient of	#72276774

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240443);