Finite Group Databasebeta

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C3×C52×A4 #11744728

order900
isoclinismisoclinic class of A4
automorphism?
homologyAbelianization (H1) = C32×C52 · Schur multiplier (H2) = C2×C3×C5

Aliases

direct productC3×C52×A4
unambiguous semidirect productC22⋊(C32×C52)
unambiguous semidirect product(C22×C3)⋊(C3×C52)
unambiguous semidirect product(C22×C5)⋊(C32×C5)
unambiguous semidirect product(C22×C3×C5)⋊(C3×C5)

Splittings

Fitting, socleC22×C3×C52 ⋊ C3
derived, SylowC22 ⋊ C32×C52
HallC22×C52 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C52A4
commutator, cosocle, hypocenterC22C32×C52
FrattiniC1G
Fitting, socleC22×C3×C52C3
LCSG ▷ C22
UCSC1 ◁ C3×C52

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 300

Conjugacy classes & character table

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

Relationships

derived subgroup ofC3⋊(C5⋊(C5⋊S4)), C5⋊D5×C3⋊S4, #72231255, …
maximal subgroup ofC3×C52×S4, C3×C5×C5⋊S4, C3×C5⋊(C5⋊S4), …
maximal normal subgroup ofC3×C52×S4, C3×C5×C5⋊S4, C3×C5⋊(C5⋊S4), …
maximal quotient ofC3×C52×SL(2,𝔽3), C2×C3×C52×A4, C52×A4×C13⋊C3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 140);