Finite Group Databasebeta

C2×#23752254 #34077695

order19328
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#23752254

Splittings

SylowC151 ⋊ C2×#428

Subgroups

subgroupG/H
centerC23C2×D604
commutatorC4×C151C23×C4
FrattiniC2×C4C23×D151
FittingC22×M16×C151C2
socleC23×C151C2×D4
prime radicalC24×C151D4
cosocleC2×C4×C151C24
hypercenterC22×M16D151
hypocenterC151C2×#428
LCSG ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

536 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3044 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 13095);