Finite Group Databasebeta

C2×#23752769 #34082401

order19328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#23752769

Splittings

SylowC151 ⋊ C2×#533

Subgroups

subgroupG/H
centerC22×C4C22×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC22×C42×C151C2
socleC23×C151C24
prime radicalC24×C151C23
hypercenterC22×C42D151
hypocenterC151C2×#533
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C22×C42

1168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

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, 17801);