Finite Group Databasebeta

C2×#23751976 #34068833

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

Aliases

direct productC2×#23751976

Splittings

SylowC151 ⋊ C2×#341

Subgroups

subgroupG/H
centerC22×C4C22⋊D151
commutatorC4×C151C2×C42
FrattiniC22×C4C22×D151
FittingC22×M16×C151C2
socleC23×C151C4⋊C4
prime radicalC24×C151Q8
cosocleC22×C4×C151C23
hypercenterC22×M16D151
hypocenterC151C2×#341
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×M16

392 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3056 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4233);