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C3×#91886 #13088490

order1440
isoclinismisoclinic class of #91885
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#91886

Splittings

FittingC3×C5×Q8 ⋊ Dic3
derivedC5×SL(2,𝔽3) ⋊ C3×C4
SylowC5 ⋊ C3×#859

Subgroups

subgroupG/H
center, hypercenterC2×C3A4⋊AGL(1,𝔽5)
commutator, hypocenterC5×SL(2,𝔽3)C3×C4
FrattiniC2C3×A4⋊AGL(1,𝔽5)
FittingC3×C5×Q8Dic3
socleC2×C3×C5SL(2,ℤ/4)
prime radicalC3×D5×SL(2,𝔽3)C2
cosocleD5×SL(2,𝔽3)C2×C3
LCSG ▷ C5×SL(2,𝔽3)
UCSC1 ◁ C2×C3

126 conjugacy classes of subgroups; only the 28 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 28 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) = 120

Conjugacy classes & character table

69 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×#72213713, C3×AGL(1,𝔽5)×GL(2,𝔽3), C2×C3×#91886, …
maximal normal subgroup ofC3×AGL(1,𝔽5)×GL(2,𝔽3), C2×C3×#91886, D3×#91886, …
maximal quotient ofC3×#72213713, C2×C3×#91886, ΓL(1,𝔽8)×#91886, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 4807);