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C5×C41×D63 #38788910

order25830
automorphism?
homologyAbelianization (H1) = C2×C5×C41 · Schur multiplier (H2) = C1

Aliases

direct productC5×C41×D63
unambiguous semidirect productC7⋊(C5×D9×C41)
unambiguous semidirect productC9⋊(C5×D7×C41)

Splittings

Fitting, HallC5×C7×C9×C41 ⋊ C2
derived, HallC7×C9 ⋊ C2×C5×C41
HallC7×C9×C41 ⋊ C2×C5
HallC5×C9×C41 ⋊ D7
HallC5×C7×C41 ⋊ D9
HallC9×C41 ⋊ C5×D7
HallC5×C7×C9 ⋊ C2×C41
HallC7×C41 ⋊ C5×D9
HallC5×C9 ⋊ D7×C41
HallC5×C7 ⋊ D9×C41
SylowC9 ⋊ C5×D7×C41
SylowC7 ⋊ C5×D9×C41

Subgroups

subgroupG/H
center, hypercenterC5×C41D63
commutator, cosocle, hypocenterC7×C9C2×C5×C41
FrattiniC3C5×C41×D21
FittingC5×C7×C9×C41C2
socleC3×C5×C7×C41D3
LCSG ▷ C7×C9
UCSC1 ◁ C5×C41

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12915

Conjugacy classes & character table

6765 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25830, 14);