Finite Group Databasebeta

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C2×C49×C11⋊C25 #41003938

order26950
automorphism?
homologyAbelianization (H1) = C2×C25×C49 · Schur multiplier (H2) = C1

Aliases

direct productC2×C49×C11⋊C25
unambiguous semidirect product(C2×C11)⋊(C25×C49)
unambiguous semidirect product(C2×C11×C49)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C25×C49
HallC2×C11×C49 ⋊ C25
HallC11×C49 ⋊ C2×C25
HallC2×C11 ⋊ C25×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49C11⋊C5
commutator, hypocenterC11C2×C25×C49
FrattiniC5×C7C2×C7×C11⋊C5
FittingC2×C5×C11×C49C5
socle, prime radicalC2×C5×C7×C11C5×C7
cosocleC5×C7×C11C2×C5×C7
LCSG ▷ C11
UCSC1 ◁ C2×C5×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26950

Conjugacy classes & character table

3430 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 5);