Finite Group Databasebeta

C4×#16861626 #30657693

order16448
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct productC4×#16861626

Splittings

derived, SylowC257 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC42#11759967
commutator, hypocenterC257C2×C4×C8
FrattiniC22C22×#11759967
FittingC42×C257C4
socleC22×C257C22×C4
prime radicalC22×D257C2×C4
cosocleC2×Dic257C23
LCSG ▷ C257
UCSC1 ◁ C42

162 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, 1505);