Finite Group Databasebeta

C22×Dic202 #15692295

order3232
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct productC22×Dic202

Splittings

SylowC101 ⋊ C22×Q8

Subgroups

subgroupG/H
centerC23C2×D101
commutator, cosocleC2×C101C24
FrattiniC2C23×D101
FittingC22×C4×C101C2
socle, prime radicalC23×C101C22
hypercenterC22×C4D101
hypocenterC101C22×Q8
LCSG ▷ C2×C101 ▷ C101
UCSC1 ◁ C23 ◁ C22×C4

156 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3232

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, 186);