Finite Group Databasebeta

D8×Dic59 #16837485

order3776
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic59

Splittings

SylowC59 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D59
commutatorC4×C59C22×C4
FrattiniC2×C4C22×D59
Fitting, prime radicalC2×D8×C59C2
socleC22×C59C2×D4
cosocleC2×C4×C59C23
hypercenterC2×D8D59
hypocenterC59C4×D8
LCSG ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1888

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3776, 632);