Finite Group Databasebeta

C2×Dic404 #15692273

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

Aliases

direct productC2×Dic404

Splittings

SylowC101 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D404
commutator, cosocleC4×C101C23
FrattiniC4C22×D101
FittingC2×C8×C101C2
socle, prime radicalC22×C101D4
hypercenterC2×C8D101
hypocenterC101C2×Q16
LCSG ▷ C4×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3232

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3232, 164);