Finite Group Databasebeta

C2×C8×C22⋊D163 #35223207

order20864
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC2×C8×C22⋊D163

Splittings

FittingC23×C8×C163 ⋊ C2
SylowC163 ⋊ C2×C8×D4

Subgroups

subgroupG/H
centerC22×C8C2×D163
commutatorC2×C163C23×C8
FrattiniC2×C4C23×D163
FittingC23×C8×C163C2
socleC23×C163C22×C4
prime radicalC22×C22⋊D163C4
cosocleC2×C4×C163C24
hypercenterC23×C8D163
hypocenterC163C2×C8×D4
LCSG ▷ C2×C163 ▷ C163
UCSC1 ◁ C22×C8 ◁ C23×C8

616 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10432

Conjugacy classes & character table

5264 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20864, 13181);