Finite Group Databasebeta

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C2×C25×C13⋊D13 #30683408

order16900
isoclinismisoclinic class of C13⋊D13
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2×C13

Aliases

direct productC2×C25×C13⋊D13
unambiguous semidirect product(C2×C13)⋊(C25×D13)

Splittings

FittingC2×C132×C25 ⋊ C2
derived, SylowC132 ⋊ C22×C25
HallC132×C25 ⋊ C22

Subgroups

subgroupG/H
center, hypercenterC2×C25C13⋊D13
commutator, hypocenterC132C22×C25
FrattiniC5C2×C5×C13⋊D13
FittingC2×C132×C25C2
socleC2×C5×C132C2×C5
prime radicalC2×C5×C13⋊D13C5
cosocleC5×C132C22×C5
LCSG ▷ C132
UCSC1 ◁ C2×C25

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8450

Conjugacy classes & character table

4300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16900, 84);