Finite Group Databasebeta

C2×#23752629 #34082209

order19328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#23752629

Splittings

SylowC151 ⋊ C2×#504

Subgroups

subgroupG/H
centerC2×C8C22×D151
commutatorC2×C151C23×C8
FrattiniC8C23×D151
FittingC2×#131×C151C2
socleC22×C151C22×C8
prime radicalC2×#41×C151C4
cosocleC8×C151C24
hypercenterC2×#131D151
hypocenterC151C2×#504
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C8 ◁ C2×#131

368 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 17609);