Finite Group Databasebeta

C2×#23751972 #34068816

order19328
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#23751972

Splittings

SylowC151 ⋊ C2×#339

Subgroups

subgroupG/H
centerC22×C4D604
commutatorC4×C151C2×C42
FrattiniC22×C4C22×D151
FittingC22×C42×C151C2
socleC23×C151C22⋊C4
prime radicalC24×C151D4
cosocleC22×C4×C151C23
hypercenterC22×C42D151
hypocenterC151C2×#339
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×C42

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

4856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4216);