Finite Group Databasebeta

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C5×D5×C11×C49 #41003958

order26950
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×D5×C11×C49
unambiguous semidirect productC5⋊(C2×C5×C11×C49)

Splittings

Fitting, HallC52×C11×C49 ⋊ C2
derivedC5 ⋊ C2×C5×C11×C49
HallC52×C49 ⋊ C2×C11
HallC52×C11 ⋊ C2×C49
SylowC52 ⋊ C2×C11×C49

Subgroups

subgroupG/H
center, hypercenterC5×C11×C49D5
commutator, hypocenterC5C2×C5×C11×C49
FrattiniC7C5×C7×D5×C11
FittingC52×C11×C49C2
socleC52×C7×C11C2×C7
prime radicalC5×C7×D5×C11C7
cosocleC5×C7C2×C5×C7×C11
LCSG ▷ C5
UCSC1 ◁ C5×C11×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

10780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 25);