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C5×Q16×SL(2,𝔽3) #14510993

order1920
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Q16×SL(2,𝔽3)
unambiguous semidirect product(Q8×Q16)⋊(C3×C5)
unambiguous semidirect product(C5×Q8×Q16)⋊C3

Splittings

Fitting, HallC5×Q8×Q16 ⋊ C3
SylowQ8×Q16 ⋊ C3×C5

Subgroups

subgroupG/H
center, socleC22×C5D4×A4
commutator, cosocleC4×Q8C22×C3×C5
FrattiniC2×C4C22×C5×A4
FittingC5×Q8×Q16C3
prime radicalC2×C5×SL(2,𝔽3)D4
hypercenterC2×C5×Q16A4
hypocenterQ8C3×C5×Q16
LCSG ▷ C4×Q8 ▷ C2×Q8 ▷ Q8
UCSC1 ◁ C22×C5 ◁ C2×C4×C5 ◁ C2×C5×Q16

242 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 640

Conjugacy classes & character table

245 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 236691);