Finite Group Databasebeta

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C32×D1495 #41002121

order26910
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×D1495
unambiguous semidirect productC5⋊(C32×D299)
unambiguous semidirect productC23⋊(C32×D65)

Splittings

Fitting, socle, HallC32×C5×C13×C23 ⋊ C2
derived, HallC5×C13×C23 ⋊ C2×C32
HallC32×C13×C23 ⋊ D5
HallC32×C5×C23 ⋊ D13
HallC32×C5×C13 ⋊ D23
HallC13×C23 ⋊ C32×D5
HallC32×C23 ⋊ D65
HallC32×C13 ⋊ D115
HallC5×C23 ⋊ C32×D13
HallC5×C13 ⋊ C32×D23
HallC32×C5 ⋊ D299
SylowC23 ⋊ C32×D65
SylowC13 ⋊ C32×D115
SylowC5 ⋊ C32×D299

Subgroups

subgroupG/H
center, hypercenterC32D1495
commutator, cosocle, hypocenterC5×C13×C23C2×C32
FrattiniC1G
Fitting, socleC32×C5×C13×C23C2
LCSG ▷ C5×C13×C23
UCSC1 ◁ C32

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13455

Conjugacy classes & character table

6741 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26910, 48);