Finite Group Databasebeta

C2×(C22⋊D151)⋊C8 #34077780

order19328
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×(C22⋊D151)⋊C8

Splittings

FittingC2×C22⋊C8×C151 ⋊ C2
SylowC151 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C4C22×D151
commutatorC2×C151C23×C8
FrattiniC2×C4C23×D151
FittingC2×C22⋊C8×C151C2
socleC23×C151C22×C4
prime radicalC22×C22⋊D151C4
cosocleC2×C4×C151C24
hypercenterC2×C22⋊C8D151
hypocenterC151C2×C8×D4
LCSG ▷ C2×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9664

Conjugacy classes & character table

3080 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19328, 13180);