Finite Group Databasebeta

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C3×C4×C5×GL(2,𝔽3) #72219471

order2880
isoclinismisoclinic class of #226
automorphism?
homologyAbelianization (H1) = C2×C3×C4×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C4×C5×GL(2,𝔽3)

Splittings

FittingC3×C4×C5×Q8 ⋊ D3
derivedSL(2,𝔽3) ⋊ C2×C3×C4×C5

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4×C5S4
commutator, hypocenterSL(2,𝔽3)C2×C3×C4×C5
FrattiniC22C2×C3×C5×S4
FittingC3×C4×C5×Q8D3
socleC22×C3×C5C2×S4
prime radicalC2×C3×C5×GL(2,𝔽3)C2
cosocleC2×SL(2,𝔽3)C22×C3×C5
LCSG ▷ SL(2,𝔽3)
UCSC1 ◁ C2×C3×C4×C5

374 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.

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

Full subgroup data →

Conjugacy classes & character table

480 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C4×C5×AGL(2,𝔽3)
maximal quotient ofC3×C4×C5×AGL(2,𝔽3)

GAP

Past the SmallGroups library coverage — no SmallGroups id.