Finite Group Databasebeta

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C11×C49×C5⋊D5 #41003962

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

Aliases

direct productC11×C49×C5⋊D5
unambiguous semidirect productC5⋊(D5×C11×C49)

Splittings

Fitting, HallC52×C11×C49 ⋊ C2
derived, SylowC52 ⋊ C2×C11×C49
HallC52×C49 ⋊ C2×C11
HallC52×C11 ⋊ C2×C49

Subgroups

subgroupG/H
center, hypercenterC11×C49C5⋊D5
commutator, hypocenterC52C2×C11×C49
FrattiniC7C7×C11×C5⋊D5
FittingC52×C11×C49C2
socleC52×C7×C11C2×C7
prime radicalC7×C11×C5⋊D5C7
cosocleC52×C7C2×C7×C11
LCSG ▷ C52
UCSC1 ◁ C11×C49

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13475

Conjugacy classes & character table

7546 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 29);