Finite Group Databasebeta

C2×#23752745 #34082375

order19328
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#23752745

Splittings

FittingC2×#126×C151 ⋊ C2
SylowC151 ⋊ C2×#529

Subgroups

subgroupG/H
centerC23C23×D151
commutator, cosocleC22×C151C25
FrattiniC22C24×D151
FittingC2×#126×C151C2
socleC23×C151C24
prime radicalC2×#18012712C2
hypercenterC2×#126D151
hypocenterC151C2×#529
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×#126

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

2156 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 17775);