#14515001

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂×C₄ · Schur multiplier (H₂) = C₁

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×#6729	C₄
cosocle	C₄×SL(2,𝔽₅)	C₂²
hypocenter	SL(2,𝔽₅)	M₁₆
LCS	G ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

185 conjugacy classes of subgroups; only the 18 normal subgroups are shown.

normal subgroups only

This group has 185 conjugacy classes of subgroups — too many to draw. Only its 18 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) = 320

Permutation generators:

(1,5,4,8,2,6,3,7)(9,10)(11,12)(13,30,21,27)(14,29,22,28)(15,32,23,26)(16,31,24,25)(17,19,18,20)(33,38,36,39,34,37,35,40)(41,42)(43,44)(45,62,53,59)(46,61,54,60)(47,64,55,58)(48,63,56,57)(49,51,50,52);(1,38,2,37)(3,40,4,39)(5,35,6,36)(7,34,8,33)(9,45,21,60,32,50,10,46,22,59,31,49)(11,47,23,57,29,52,12,48,24,58,30,51)(13,56,28,62,18,43,14,55,27,61,17,44)(15,53,25,64,20,42,16,54,26,63,19,41)

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, 240699);