Finite Group Databasebeta

C2×#23752046 #34071402

order19328
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#23752046

Splittings

SylowC151 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C16C2×D151
commutatorC2×C151C22×C16
FrattiniC16C22×D151
FittingC22×C16×C151C2
socleC22×C151C2×C16
prime radicalC23×C151C16
cosocleC16×C151C23
hypercenterC22×C16D151
hypocenterC151C2×M64
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C16 ◁ C22×C16

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 6802);