Finite Group Databasebeta

C2×#23751982 #34068851

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

Aliases

direct productC2×#23751982

Splittings

SylowC151 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4(C2×D151)⋊C4
commutatorC22×C151C2×C42
FrattiniC22×C4C22×D151
FittingC2×#117×C151C2
socleC22×C151#95
prime radicalC24×C151C2×C4
cosocleC22×C4×C151C23
hypercenterC2×#117D151
hypocenterC151C2×#344
LCSG ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#117

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 4832

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 4251);