#14515008

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

Aliases

No aliases for this group.

Subgroups

	subgroup	G/H
center, socle	C₂²	C₂²⋊S₅
commutator, cosocle	C₄×SL(2,𝔽₅)	C₂²
Frattini	C₂×C₄	C₂×S₅
Fitting, hypercenter	C₄⋊C₄	S₅
prime radical	C₄⋊#6732	C₂
hypocenter	SL(2,𝔽₅)	D₈
LCS	G ▷ C₄×SL(2,𝔽₅) ▷ C₂×SL(2,𝔽₅) ▷ SL(2,𝔽₅)
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

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

normal subgroups only

This group has 197 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) = 192

Permutation generators:

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

Conjugacy classes & character table

45 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240706);