Finite Group Databasebeta

C2×#23752040 #34070890

order19328
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#23752040

Splittings

SylowC151 ⋊ C2×#367

Subgroups

subgroupG/H
centerC23D1208
commutatorC8×C151C22×C4
FrattiniC2×C8C22×D151
FittingC22×C16×C151C2
socle, prime radicalC23×C151D8
cosocleC2×C8×C151C23
hypercenterC22×C16D151
hypocenterC151C2×#367
LCSG ▷ C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19328

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, 6290);