Finite Group Databasebeta

C22×D269⋊C8 #31771676

order17216
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×D269⋊C8
unambiguous semidirect productD269⋊(C22×C8)

Splittings

derived, SylowC269 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11761640
commutator, hypocenterC269C23×C8
FrattiniC2C23×#11761640
FittingC22×C4×C269C4
socleC23×C269C2×C4
prime radicalC23×D269C4
cosocleDic269C24
LCSG ▷ C269
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8608

Conjugacy classes & character table

1136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17216, 1620);