#14514937

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, Frattini	C₂×C₄	C₂×S₅
commutator	C₂×SL(2,𝔽₅)	C₂×C₄
Fitting, hypercenter	C₂×C₈	S₅
socle	C₂²	C₄×S₅
prime radical	C₂×#91870	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

296 conjugacy classes of subgroups; only the 20 normal subgroups are shown.

normal subgroups only

This group has 296 conjugacy classes of subgroups — too many to draw. Only its 20 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:

(1,27)(2,28)(3,47,23,32,20,41)(4,48,24,31,19,42)(5,35,16,34,22,43)(6,36,15,33,21,44)(7,38,18,40,10,52)(8,37,17,39,9,51)(11,49,13,46,25,29)(12,50,14,45,26,30);(3,23,5,9)(4,24,6,10)(7,18,13,20)(8,17,14,19)(11,21,12,22)(27,28)(29,50,31,36)(30,49,32,35)(33,43,39,45)(34,44,40,46)(37,48,38,47)(41,42)(51,52)

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240635);