Finite Group Databasebeta

C22×#18012679 #34082206

order19328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC22×#18012679

Splittings

SylowC151 ⋊ C22×M32

Subgroups

subgroupG/H
centerC22×C8C2×D151
commutatorC2×C151C23×C8
FrattiniC8C23×D151
FittingC23×C8×C151C2
socleC23×C151C2×C8
prime radicalC24×C151C8
cosocleC8×C151C24
hypercenterC23×C8D151
hypocenterC151C22×M32
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C8 ◁ C23×C8

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

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, 17606);