Finite Group Databasebeta

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C49×D11⋊C25 #41003935

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

Aliases

direct productC49×D11⋊C25
unambiguous semidirect productD11⋊(C25×C49)
unambiguous semidirect product(C11⋊C25)⋊(C2×C49)
unambiguous semidirect product(D11×C49)⋊C25

Splittings

derived, SylowC11 ⋊ C2×C25×C49
HallC49×C11⋊C25 ⋊ C2
HallD11×C49 ⋊ C25
HallC11×C49 ⋊ C2×C25
HallC11⋊C25 ⋊ C2×C49
HallD11 ⋊ C25×C49

Subgroups

subgroupG/H
center, hypercenterC5×C49AGL(1,𝔽11)
commutator, hypocenterC11C2×C25×C49
FrattiniC5×C7C7×AGL(1,𝔽11)
FittingC5×C11×C49C2×C5
socle, cosocleC5×C7×C11C2×C5×C7
prime radicalC5×C7×D11C5×C7
LCSG ▷ C11
UCSC1 ◁ C5×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 13475

Conjugacy classes & character table

2695 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26950, 2);