Finite Group Databasebeta

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C2×C32×D41⋊C25 #49146705

order36900
automorphism?
homologyAbelianization (H1) = C22×C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C32×D41⋊C25
unambiguous semidirect productD41⋊(C2×C32×C25)
unambiguous semidirect product(C2×D41)⋊(C32×C25)
unambiguous semidirect product(C2×C3×D41)⋊(C3×C25)
unambiguous semidirect product(C41⋊C25)⋊(C22×C32)
unambiguous semidirect product(C2×C32×D41)⋊C25
unambiguous semidirect product(C2×C41⋊C25)⋊(C2×C32)

Splittings

derived, SylowC41 ⋊ C22×C32×C25
HallC32×C41⋊C25 ⋊ C22
HallC2×C32×D41 ⋊ C25
HallC41⋊C25 ⋊ C22×C32
HallC32×C41 ⋊ C22×C25
HallC2×D41 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D41⋊C5
commutator, hypocenterC41C22×C32×C25
FrattiniC5C2×C32×D41⋊C5
Fitting, socleC2×C32×C5×C41C2×C5
prime radicalC2×C32×C5×D41C5
cosocleC5×C41C22×C32×C5
LCSG ▷ C41
UCSC1 ◁ C2×C32×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18450

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 106);