Finite Group Databasebeta

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C2×C3⋊D3×C25×C29 #39907889

order26100
automorphism?
homologyAbelianization (H1) = C22×C25×C29 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C3⋊D3×C25×C29
unambiguous semidirect product(C2×C3)⋊(D3×C25×C29)

Splittings

FittingC2×C32×C25×C29 ⋊ C2
derived, SylowC32 ⋊ C22×C25×C29
HallC32×C25×C29 ⋊ C22
HallC32×C29 ⋊ C22×C25
HallC32×C25 ⋊ C22×C29

Subgroups

subgroupG/H
center, hypercenterC2×C25×C29C3⋊D3
commutator, hypocenterC32C22×C25×C29
FrattiniC5C2×C5×C3⋊D3×C29
FittingC2×C32×C25×C29C2
socleC2×C32×C5×C29C2×C5
prime radicalC2×C5×C3⋊D3×C29C5
cosocleC32×C5C22×C5×C29
LCSG ▷ C32
UCSC1 ◁ C2×C25×C29

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13050

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26100, 123);