#14514910

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂⁴ · Schur multiplier (H₂) = C₂⁶

Aliases

No aliases for this group.

Splittings

Fitting

#41 ⋊ S₅

Subgroups

	subgroup	G/H
center, Frattini	C₂	C₂³×S₅
commutator, socle, cosocle	C₂×A₅	C₂⁴
Fitting, hypercenter	#41	S₅
hypocenter	A₅	2₋¹⁺⁴
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ #41

1316 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 1316 conjugacy classes of subgroups — too many to draw. Only its 85 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) = 48

Permutation generators:

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

Conjugacy classes & character table

61 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240608);