Finite Group Databasebeta

C22×#16861626 #30657808

order16448
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C26

Aliases

direct productC22×#16861626

Splittings

derived, SylowC257 ⋊ C23×C8

Subgroups

subgroupG/H
center, hypercenterC22×C4#11759967
commutator, hypocenterC257C23×C8
FrattiniC2C23×#11759967
FittingC22×C4×C257C4
socleC23×C257C2×C4
prime radicalC23×D257C4
cosocleDic257C24
LCSG ▷ C257
UCSC1 ◁ C22×C4

338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

1088 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1620);