#14514907

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	H(5,𝔽₂)
LCS	G ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₂ ◁ #41

1456 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 1456 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) = 40

Permutation generators:

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

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, 240605);