Finite Group Databasebeta

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C25×D693 #46831372

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

Aliases

direct productC25×D693
unambiguous semidirect productC7⋊(C25×D99)
unambiguous semidirect productC9⋊(C25×D77)

Splittings

Fitting, HallC7×C9×C11×C25 ⋊ C2
derived, HallC7×C9×C11 ⋊ C2×C25
HallC9×C11×C25 ⋊ D7
HallC7×C11×C25 ⋊ D9
HallC7×C9×C25 ⋊ D11
HallC11×C25 ⋊ D63
HallC9×C25 ⋊ D77
HallC7×C25 ⋊ D99
HallC9×C11 ⋊ D7×C25
HallC7×C11 ⋊ D9×C25
HallC7×C9 ⋊ D11×C25
SylowC11 ⋊ C25×D63
SylowC9 ⋊ C25×D77
SylowC7 ⋊ C25×D99

Subgroups

subgroupG/H
center, hypercenterC25D693
commutator, hypocenterC7×C9×C11C2×C25
FrattiniC3×C5C5×D231
FittingC7×C9×C11×C25C2
socleC3×C5×C7×C11C5×D3
prime radicalC5×D693C5
cosocleC5×C7×C9×C11C2×C5
LCSG ▷ C7×C9×C11
UCSC1 ◁ C25

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17325

Conjugacy classes & character table

8700 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34650, 15);