Finite Group Databasebeta

C2×#13108061 #15692268

order3232
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13108061

Splittings

FittingC2×Q8×C101 ⋊ C2
SylowC101 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22C22⋊D101
commutator, cosocleC4×C101C23
FrattiniC4C22×D101
FittingC2×Q8×C101C2
socleC22×C101D4
prime radicalC2×D404C2
hypercenterC2×Q8D101
hypocenterC101C2×SD16
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 159);