Finite Group Databasebeta

C2×#23751987 #34070699

order19328
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#23751987

Splittings

SylowC151 ⋊ C2×#346

Subgroups

subgroupG/H
centerC22×C8C2×D151
commutatorC2×C151C2×C4×C8
FrattiniC2×C8C22×D151
FittingC22×C16×C151C2
socle, prime radicalC23×C151C2×C8
cosocleC2×C8×C151C23
hypercenterC22×C16D151
hypocenterC151C2×#346
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C8 ◁ C22×C16

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19328

Conjugacy classes & character table

4880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 6099);