Finite Group Databasebeta

#103×Dic163 #35214358

order20864
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4

Aliases

direct product#103×Dic163

Splittings

SylowC163 ⋊ C4×#103

Subgroups

subgroupG/H
centerC23D4×D163
commutatorC4×C163C2×C42
FrattiniC22×C4C22×D163
FittingC2×#103×C163C2
socle, prime radicalC23×C163C2×D4
cosocleC22×C4×C163C23
hypercenterC2×#103D163
hypocenterC163C4×#103
LCSG ▷ C4×C163 ▷ C2×C163 ▷ C163
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

332 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 20864

Conjugacy classes & character table

2324 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 4332);