#14515011

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	C₂×SL(2,𝔽₅)	D₄
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

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

normal subgroups only

This group has 164 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) = 384

Permutation generators:

(1,16,6,17,7,4,21,5,12,13)(2,18,3,15,10,8,19,9,14,11)(20,24)(22,23)(25,30,27,32,26,29,28,31)(33,56,45,47,50,36,52,39,46,51)(34,55,43,44,53,40,54,42,49,48)(35,41)(37,38)(57,63,60,61,58,64,59,62);(1,35,17,43,4,41,12,42)(2,37,15,39,8,38,14,45)(3,36,6,34,9,33,5,40)(7,46,23,56,13,47,22,52)(10,49,20,55,11,44,24,54)(16,50,18,53,21,51,19,48)(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, 240709);