Finite Group Databasebeta

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C32×C5×D5×C41 #32914428

order18450
automorphism?
homologyAbelianization (H1) = C2×C32×C5×C41 · Schur multiplier (H2) = C3

Aliases

direct productC32×C5×D5×C41
unambiguous semidirect productC5⋊(C2×C32×C5×C41)

Splittings

Fitting, socle, HallC32×C52×C41 ⋊ C2
derivedC5 ⋊ C2×C32×C5×C41
HallC52×C41 ⋊ C2×C32
HallC32×C52 ⋊ C2×C41
SylowC52 ⋊ C2×C32×C41

Subgroups

subgroupG/H
center, hypercenterC32×C5×C41D5
commutator, cosocle, hypocenterC5C2×C32×C5×C41
FrattiniC1G
Fitting, socleC32×C52×C41C2
LCSG ▷ C5
UCSC1 ◁ C32×C5×C41

120 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3690

Conjugacy classes & character table

7380 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC32×C5×D5×D41, C32×C5×AGL(1,𝔽5)×C41, C32×C5×#11717963, …
maximal normal subgroup ofC32×C5×D5×D41, C32×C5×AGL(1,𝔽5)×C41, C32×C5×#11717963, …
maximal quotient ofC32×C5×Dic5×C41, C2×C32×C5×D5×C41

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18450, 97);