Finite Group Databasebeta

C4×#16861627 #30657698

order16448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4

Aliases

direct productC4×#16861627

Splittings

SylowC257 ⋊ C4×M16

Subgroups

subgroupG/H
centerC2×C4C2×#11759967
commutatorC2×C257C2×C42
FrattiniC22C22×#11759967
FittingC22×C4×C257C4
socleC22×C257C22×C4
prime radicalC23×C257C2×C4
cosocleC2×Dic257C23
hypercenterC22×C4#11759967
hypocenterC257C4×M16
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C2×C4 ◁ C22×C4

142 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, 1510);