Finite Group Databasebeta

C2×C22⋊#14523346 #30657704

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

Aliases

direct productC2×C22⋊#14523346

Splittings

SylowC257 ⋊ C2×C22⋊C8

Subgroups

subgroupG/H
centerC23C2×#11759967
commutatorC2×C257C22×C8
FrattiniC22C22×#11759967
Fitting, prime radicalC24×C257C4
socleC23×C257C2×C4
cosocleC2×Dic257C23
hypercenterC24#11759967
hypocenterC257C2×C22⋊C8
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C23 ◁ C24

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, 1516);