Finite Group Databasebeta

C2×D509⋊C16 #45656292

order32576
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C23

Aliases

direct productC2×D509⋊C16
unambiguous semidirect productD509⋊(C2×C16)

Splittings

derived, SylowC509 ⋊ C22×C16

Subgroups

subgroupG/H
center, hypercenterC2×C8#14523266
commutator, hypocenterC509C22×C16
FrattiniC4C22×#14523266
FittingC2×C8×C509C4
socleC22×C509C2×C8
prime radicalC22×D509C8
cosocle#16861325C23
LCSG ▷ C509
UCSC1 ◁ C2×C8

98 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16288

Conjugacy classes & character table

2096 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 1603);