Finite Group Databasebeta

← Prev (#14514913) Next (#14514915) →

SL(2,𝔽5)⋊C16 #14514914

order1920
automorphism?
homologyAbelianization (H1) = C16 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productSL(2,𝔽5)⋊C16

Splittings

derivedSL(2,𝔽5) ⋊ C16

Subgroups

subgroupG/H
center, Frattini, Fitting, hypercenterC2×C8S5
commutator, hypocenterSL(2,𝔽5)C16
socleC22A5⋊C8
prime radicalC2×SL(2,𝔽5)C8
cosocleC8×SL(2,𝔽5)C2
LCSG ▷ SL(2,𝔽5)
UCSC1 ◁ C2×C8

99 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 384

Permutation generators:

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

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240612);