#14514873

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

non-solvable

Aliases

No aliases for this group.

Splittings

Fitting

#41 ⋊ S₅

Subgroups

	subgroup	G/H
center	C₄	C₂²⋊S₅
commutator, cosocle	C₄×A₅	C₂³
Frattini	C₄	C₂²×S₅
Fitting, hypercenter	#41	S₅
socle	C₂×A₅	C₂×D₄
hypocenter	A₅	#135
LCS	G ▷ C₄×A₅ ▷ C₂×A₅ ▷ A₅
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #41

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

normal subgroups only

This group has 521 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) = 80

Permutation generators:

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

Conjugacy classes & character table

52 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240571);