Finite Group Databasebeta

← Prev (#14510973) Next (#14510975) →

C5×M16×SL(2,𝔽3) #14510974

order1920
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×M16×SL(2,𝔽3)
unambiguous semidirect product(Q8×M16)⋊(C3×C5)
unambiguous semidirect product(C5×Q8×M16)⋊C3

Splittings

Fitting, HallC5×Q8×M16 ⋊ C3
SylowQ8×M16 ⋊ C3×C5

Subgroups

subgroupG/H
centerC2×C4×C5C22×A4
commutatorC2×Q8C2×C3×C4×C5
FrattiniC2×C4C22×C5×A4
FittingC5×Q8×M16C3
socleC22×C5C2×C4×A4
prime radicalC22×C5×SL(2,𝔽3)C4
cosocleC4×Q8C22×C3×C5
hypercenterC2×C5×M16A4
hypocenterQ8C3×C5×M16
LCSG ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C2×C4×C5 ◁ C2×C5×M16

276 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 276 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

350 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236672);