Finite Group Databasebeta

C2×#23752208 #34077606

order19328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#23752208

Splittings

SylowC151 ⋊ C2×#416

Subgroups

subgroupG/H
centerC22×C4C22⋊D151
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
Fitting, prime radicalC22×#41×C151C2
socleC23×C151C2×D4
cosocleC2×C4×C151C24
hypercenterC22×#41D151
hypocenterC151C2×#416
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

792 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, 13006);