Finite Group Databasebeta

C2×#22551649 #30657706

order16448
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C24

Aliases

direct productC2×#22551649

Splittings

SylowC257 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#11759967
commutatorC2×C257C22×C8
FrattiniC22C22×#11759967
FittingC22×C4×C257C4
socleC23×C257C2×C4
prime radicalC23×D257C4
cosocleC2×Dic257C23
hypercenterC22×C4#11759967
hypocenterC257C2×C22⋊C8
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C23 ◁ C22×C4

202 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, 1518);