Finite Group Databasebeta

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C2×C3⋊(C3⋊(D41⋊C25)) #49146708

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

Aliases

direct productC2×C3⋊(C3⋊(D41⋊C25))
unambiguous semidirect product(C2×C3)⋊(C3⋊(D41⋊C25))
unambiguous semidirect product(C2×C3⋊D123)⋊C25
unambiguous semidirect product(C2×C41⋊C25)⋊(C3⋊D3)

Splittings

derived, HallC32×C41 ⋊ C22×C25
HallC32×C41⋊C25 ⋊ C22
HallC2×C3⋊D123 ⋊ C25
HallC41⋊C25 ⋊ C2×C3⋊D3
SylowC41 ⋊ C2×C3⋊D3×C25
SylowC32 ⋊ C2×D41⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(C3⋊(D41⋊C5))
commutator, hypocenterC32×C41C22×C25
FrattiniC5C2×C3⋊(C3⋊(D41⋊C5))
Fitting, socleC2×C32×C5×C41C2×C5
prime radicalC2×C5×C3⋊D123C5
cosocleC32×C5×C41C22×C5
LCSG ▷ C32×C41
UCSC1 ◁ C2×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18450

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36900, 109);