Finite Group Databasebeta

C2×#23752042 #34070902

order19328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#23752042

Splittings

SylowC151 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D1208
commutatorC8×C151C22×C4
FrattiniC2×C8C22×D151
FittingC22×C16×C151C2
socleC22×C151#107
prime radicalC23×C151Q16
cosocleC2×C8×C151C23
hypercenterC22×C16D151
hypocenterC151C2×#368
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

4844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 6302);