Finite Group Databasebeta

C22×#16861627 #30657809

order16448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC22×#16861627

Splittings

SylowC257 ⋊ C22×M16

Subgroups

subgroupG/H
centerC23C2×#11759967
commutatorC2×C257C23×C4
FrattiniC2C23×#11759967
Fitting, prime radicalC24×C257C4
socleC23×C257C2×C4
cosocleDic257C24
hypercenterC24#11759967
hypocenterC257C22×M16
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C23 ◁ C24

298 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

1064 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1621);