Finite Group Databasebeta

D8×Dic41 #14580419

order2624
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic41

Splittings

SylowC41 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D41
commutatorC4×C41C22×C4
FrattiniC2×C4C22×D41
Fitting, prime radicalC2×D8×C41C2
socleC22×C41C2×D4
cosocleC2×C4×C41C23
hypercenterC2×D8D41
hypocenterC41C4×D8
LCSG ▷ C4×C41 ▷ C2×C41 ▷ C41
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1312

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2624, 632);