#14515010

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
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

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

normal subgroups only

This group has 212 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:

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

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, 240708);