Finite Group Databasebeta

C2×#13108059 #15692265

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

Aliases

direct productC2×#13108059

Splittings

FittingC2×D4×C101 ⋊ C2
SylowC101 ⋊ C2×D8

Subgroups

subgroupG/H
centerC22C22⋊D101
commutator, cosocleC4×C101C23
FrattiniC4C22×D101
FittingC2×D4×C101C2
socleC22×C101D4
hypercenterC2×D4D101
hypocenterC101C2×D8
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D4

76 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, 156);