#14514932

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, socle	C₂²	C₂²⋊S₅
commutator	#6732	C₂×C₄
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×D₄	S₅
prime radical	C₂×#91881	C₂
cosocle	C₂×#6732	C₂²
hypocenter	SL(2,𝔽₅)	C₂²⋊C₄
LCS	G ▷ #6732 ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₄

358 conjugacy classes of subgroups; only the 22 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 22 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:

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

Conjugacy classes & character table

48 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240630);