#14514727

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	C₂×C₈	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 ◁ C₂×C₈

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

normal subgroups only

This group has 317 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) = 96

Permutation generators:

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

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, 240425);