Finite Group Databasebeta

C2×#13108057 #15692259

order3232
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#13108057

Splittings

FittingC2×C8×C101 ⋊ C2
SylowC101 ⋊ C2×M16

Subgroups

subgroupG/H
centerC2×C4C2×D101
commutatorC2×C101C22×C4
FrattiniC4C22×D101
FittingC2×C8×C101C2
socleC22×C101C2×C4
prime radicalC22×D101C4
cosocleC4×C101C23
hypercenterC2×C8D101
hypocenterC101C2×M16
LCSG ▷ C2×C101 ▷ C101
UCSC1 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1616

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 150);