Finite Group Databasebeta

D8×Dic359 #37526526

order22976
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productD8×Dic359

Splittings

SylowC359 ⋊ C4×D8

Subgroups

subgroupG/H
centerC22D4×D359
commutatorC4×C359C22×C4
FrattiniC2×C4C22×D359
Fitting, prime radicalC2×D8×C359C2
socleC22×C359C2×D4
cosocleC2×C4×C359C23
hypercenterC2×D8D359
hypocenterC359C4×D8
LCSG ▷ C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11488

Conjugacy classes & character table

2534 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22976, 632);