Finite Group Databasebeta

C2×#30633804 #44569669

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

Aliases

direct productC2×#30633804

Splittings

SylowC1013 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22C22⋊D1013
commutator, cosocleC4×C1013C23
FrattiniC4C22×D1013
FittingC2×Q8×C1013C2
socle, prime radicalC22×C1013D4
hypercenterC2×Q8D1013
hypocenterC1013C2×Q16
LCSG ▷ C4×C1013 ▷ C2×C1013 ▷ C1013
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 32416

Conjugacy classes & character table

5074 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32416, 163);