Finite Group Databasebeta

C22×D317⋊C8 #35204294

order20288
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D317⋊C8
unambiguous semidirect productD317⋊(C22×C8)

Splittings

derived, SylowC317 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11929639
commutator, hypocenterC317C23×C8
FrattiniC2C23×#11929639
FittingC22×C4×C317C4
socleC23×C317C2×C4
prime radicalC23×D317C4
cosocleDic317C24
LCSG ▷ C317
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10144

Conjugacy classes & character table

1328 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20288, 1620);