Finite Group Databasebeta

D8×#11745659 #28560106

order15104
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productD8×#11745659

Splittings

FittingC8×D8×C59 ⋊ C2
SylowC59 ⋊ M16×D8

Subgroups

subgroupG/H
centerC2×C4C2×D4×D59
commutatorC2×C4×C59C23×C4
FrattiniC42C23×D59
FittingC8×D8×C59C2
socleC22×C59C2×C4×D4
prime radicalC2×D8×D59C4
cosocleC42×C59C24
hypercenterC8×D8D59
hypocenterC59M16×D8
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ C8×D8

794 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3776

Conjugacy classes & character table

1694 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15104, 140985);