Finite Group Databasebeta

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C32×C7×D205 #38788974

order25830
automorphism?
homologyAbelianization (H1) = C2×C32×C7 · Schur multiplier (H2) = C3

Aliases

direct productC32×C7×D205
unambiguous semidirect productC5⋊(C32×C7×D41)
unambiguous semidirect productC41⋊(C32×C7×D5)

Splittings

Fitting, socle, HallC32×C5×C7×C41 ⋊ C2
derived, HallC5×C41 ⋊ C2×C32×C7
HallC32×C7×C41 ⋊ D5
HallC32×C5×C41 ⋊ C2×C7
HallC5×C7×C41 ⋊ C2×C32
HallC32×C41 ⋊ C7×D5
HallC32×C5×C7 ⋊ D41
HallC7×C41 ⋊ C32×D5
HallC32×C5 ⋊ C7×D41
SylowC41 ⋊ C32×C7×D5
HallC5×C7 ⋊ C32×D41
SylowC5 ⋊ C32×C7×D41

Subgroups

subgroupG/H
center, hypercenterC32×C7D205
commutator, cosocle, hypocenterC5×C41C2×C32×C7
FrattiniC1G
Fitting, socleC32×C5×C7×C41C2
LCSG ▷ C5×C41
UCSC1 ◁ C32×C7

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

6552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 78);