Finite Group Databasebeta

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C5×Dic3×SL(2,𝔽3) #13086231

order1440
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic3×SL(2,𝔽3)
unambiguous semidirect productC3⋊(C4×C5×SL(2,𝔽3))
unambiguous semidirect product(Q8×Dic3)⋊(C3×C5)
unambiguous semidirect product(C5×Q8×Dic3)⋊C3

Splittings

derivedC3×Q8 ⋊ C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC22×C5D3×A4
commutator, hypocenterC3×Q8C3×C4×C5
FrattiniC22C5×D3×A4
FittingC2×C3×C5×Q8C2×C3
socleC22×C3×C5C2×A4
prime radicalC2×C3×C5×SL(2,𝔽3)C2
cosocleC2×C3×Q8C2×C3×C5
LCSG ▷ C3×Q8
UCSC1 ◁ C22×C5

134 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 46 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) = 480

Conjugacy classes & character table

210 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 2548);