Finite Group Databasebeta

C2×#31775397 #46853449

order34912
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31775397

Splittings

FittingC2×C8×C1091 ⋊ C2
SylowC1091 ⋊ C2×SD16

Subgroups

subgroupG/H
centerC22D4364
commutator, cosocleC4×C1091C23
FrattiniC4C22×D1091
FittingC2×C8×C1091C2
socleC22×C1091D4
prime radicalC2×D4364C2
hypercenterC2×C8D1091
hypocenterC1091C2×SD16
LCSG ▷ C4×C1091 ▷ C2×C1091 ▷ C1091
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

68 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17456

Conjugacy classes & character table

8734 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34912, 161);