Finite Group Databasebeta

C2×#23752177 #34077548

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

Aliases

direct productC2×#23752177

Splittings

FittingC2×C22⋊C8×C151 ⋊ C2
SylowC151 ⋊ C2×#408

Subgroups

subgroupG/H
centerC22×C4C22×D151
commutatorC22×C151C23×C4
FrattiniC2×C4C23×D151
FittingC2×C22⋊C8×C151C2
socleC23×C151C22×C4
prime radicalC22×#14559004C2
cosocleC2×C4×C151C24
hypercenterC2×C22⋊C8D151
hypocenterC151C2×#408
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

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, 12948);