Finite Group Databasebeta

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C3×C49×C61⋊C3 #41002005

order26901
automorphism?
homologyAbelianization (H1) = C32×C49 · Schur multiplier (H2) = C3

Aliases

direct productC3×C49×C61⋊C3
unambiguous semidirect productC61⋊(C32×C49)
unambiguous semidirect product(C3×C61)⋊(C3×C49)

Splittings

FittingC3×C49×C61 ⋊ C3
derived, SylowC61 ⋊ C32×C49
HallC49×C61 ⋊ C32

Subgroups

subgroupG/H
center, hypercenterC3×C49C61⋊C3
commutator, hypocenterC61C32×C49
FrattiniC7C3×C7×C61⋊C3
FittingC3×C49×C61C3
socleC3×C7×C61C3×C7
prime radicalC3×C7×C61⋊C3C7
cosocleC7×C61C32×C7
LCSG ▷ C61
UCSC1 ◁ C3×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8967

Conjugacy classes & character table

3381 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26901, 11);