Finite Group Databasebeta

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C11×C25×D63 #46831371

order34650
automorphism?
homologyAbelianization (H1) = C2×C11×C25 · Schur multiplier (H2) = C1

Aliases

direct productC11×C25×D63
unambiguous semidirect productC7⋊(C11×D9×C25)
unambiguous semidirect productC9⋊(C11×D7×C25)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC7×C9 ⋊ C2×C11×C25
HallC9×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ D9
HallC7×C9×C25 ⋊ C2×C11
HallC7×C9×C11 ⋊ C2×C25
HallC9×C25 ⋊ C11×D7
HallC7×C25 ⋊ C11×D9
HallC9×C11 ⋊ D7×C25
HallC7×C11 ⋊ D9×C25
SylowC9 ⋊ C11×D7×C25
SylowC7 ⋊ C11×D9×C25

Subgroups

subgroupG/H
center, hypercenterC11×C25D63
commutator, hypocenterC7×C9C2×C11×C25
FrattiniC3×C5C5×C11×D21
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C5×D3
prime radicalC5×C11×D63C5
cosocleC5×C7×C9C2×C5×C11
LCSG ▷ C7×C9
UCSC1 ◁ C11×C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

9075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 14);