Finite Group Databasebeta

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C31⋊C3×D145 #41004213

order26970
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

direct productC31⋊C3×D145
unambiguous semidirect productC5⋊(D29×C31⋊C3)
unambiguous semidirect productC29⋊(D5×C31⋊C3)
unambiguous semidirect product(C31×D145)⋊C3

Splittings

Fitting, socle, derived, HallC5×C29×C31 ⋊ C2×C3
HallC5×C29×C31⋊C3 ⋊ C2
HallC31×D145 ⋊ C3
HallC29×C31⋊C3 ⋊ D5
HallC29×C31 ⋊ C3×D5
HallC5×C31⋊C3 ⋊ D29
HallC5×C31 ⋊ C3×D29
HallC5×C29 ⋊ C2×C31⋊C3
SylowC31 ⋊ C3×D145
SylowC29 ⋊ D5×C31⋊C3
SylowC5 ⋊ D29×C31⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C29×C31C2×C3
LCSG ▷ C5×C29×C31
UCSC1

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4495

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26970, 32);