Finite Group Databasebeta

C2×#30654303 #45656315

order32576
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#30654303

Splittings

SylowC509 ⋊ C2×#131

Subgroups

subgroupG/H
centerC22C22×#14523266
commutatorC2×C509C23×C4
FrattiniC2C23×#14523266
FittingC2×Q8×C509C4
socleC22×C509C22×C4
prime radicalC2×#22550862C2
cosocleDic509C24
hypercenterC2×Q8#14523266
hypocenterC509C2×#131
LCSG ▷ C2×C509 ▷ C509
UCSC1 ◁ C22 ◁ C2×Q8

266 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16288

Conjugacy classes & character table

1310 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32576, 1626);