Finite Group Databasebeta

C2×Dic4132 #45683148

order33056
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×Dic4132

Splittings

SylowC1033 ⋊ C2×Q16

Subgroups

subgroupG/H
centerC22D4132
commutator, cosocleC4×C1033C23
FrattiniC4C22×D1033
FittingC2×C8×C1033C2
socle, prime radicalC22×C1033D4
hypercenterC2×C8D1033
hypocenterC1033C2×Q16
LCSG ▷ C4×C1033 ▷ C2×C1033 ▷ C1033
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 33056

Conjugacy classes & character table

8270 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33056, 164);