#14515012

order	1920
automorphism	?
homology	Abelianization (H₁) = C₂² · Schur multiplier (H₂) = C₂

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₄⋊S₅
commutator, cosocle	C₄×SL(2,𝔽₅)	C₂²
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₂×C₈	S₅
prime radical	C₄⋊#6729	C₂
hypocenter	SL(2,𝔽₅)	D₈
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈

179 conjugacy classes of subgroups; only the 16 normal subgroups are shown.

normal subgroups only

This group has 179 conjugacy classes of subgroups — too many to draw. Only its 16 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:

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

Conjugacy classes & character table

51 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240710);