Finite Group Databasebeta

C2×D1013⋊C8 #44569735

order32416
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×D1013⋊C8
unambiguous semidirect productD1013⋊(C2×C8)

Splittings

derived, SylowC1013 ⋊ C22×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4#16860990
commutator, hypocenterC1013C22×C8
FrattiniC2C22×#16860990
FittingC2×C4×C1013C4
socleC22×C1013C2×C4
prime radicalC22×D1013C4
cosocleDic1013C23
LCSG ▷ C1013
UCSC1 ◁ C2×C4

76 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16208

Conjugacy classes & character table

2056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32416, 229);