Finite Group Databasebeta

D8×Dic491 #44536808

order31424
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic491

Splittings

SylowC491 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D491
commutatorC4×C491C22×C4
FrattiniC2×C4C22×D491
Fitting, prime radicalC2×D8×C491C2
socleC22×C491C2×D4
cosocleC2×C4×C491C23
hypercenterC2×D8D491
hypocenterC491C4×D8
LCSG ▷ C4×C491 ▷ C2×C491 ▷ C491
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15712

Conjugacy classes & character table

3458 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31424, 632);