Finite Group Databasebeta

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C2×C3×#91185 #72219151

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

Aliases

direct productC2×C3×#91185

Splittings

derivedC5×SL(2,𝔽3) ⋊ C2×C3×C4
SylowC5 ⋊ C2×C3×GU(2,𝔽3)

Subgroups

subgroupG/H
center, hypercenterC2×C3×C4C5⋊S4
commutator, hypocenterC5×SL(2,𝔽3)C2×C3×C4
FrattiniC4C2×C3×C5⋊S4
FittingC2×C3×C5×#41D3
socleC22×C3×C5SL(2,ℤ/4)
prime radicalC2×C3×C5×#41⋊C3C2
cosocleC5×#41⋊C3C22×C3
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C3×C4

350 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 78 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

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

GAP

Past the SmallGroups library coverage — no SmallGroups id.