Finite Group Databasebeta

C2×#23752050 #34071411

order19328
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#23752050

Splittings

SylowC151 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#18012680
commutator, cosocleC16×C151C23
FrattiniC16C22×D151
Fitting, prime radicalC2×D16×C151C2
socleC22×C151D16
hypercenterC2×D16D151
hypocenterC151C2×SD64
LCSG ▷ C16×C151 ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

1688 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 6811);