Finite Group Databasebeta

C2×D16×Dic59 #28741950

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×D16×Dic59

Splittings

SylowC59 ⋊ C2×C4×D16

Subgroups

subgroupG/H
centerC23D8×D59
commutatorC8×C59C23×C4
FrattiniC2×C8C23×D59
Fitting, prime radicalC22×D16×C59C2
socleC23×C59C2×D8
cosocleC2×C8×C59C24
hypercenterC22×D16D59
hypocenterC59C2×C4×D16
LCSG ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C22×D16

806 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7552

Conjugacy classes & character table

1364 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 322829);