Finite Group Databasebeta

← Prev (#30657846) Next (#30657848) →

C2×C4×#14523348 #30657847

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

Aliases

direct productC2×C4×#14523348
unambiguous semidirect product#11759967⋊(C2×C8)

Splittings

FittingC2×C4×C257 ⋊ C8
derived, SylowC257 ⋊ C2×C4×C8

Subgroups

subgroupG/H
center, hypercenterC2×C4#14523348
commutator, hypocenterC257C2×C4×C8
FrattiniC2C22×#14523348
FittingC2×C4×C257C8
socleC22×C257C2×C8
prime radicalC22×D257C2×C4
cosocleC2×#11759967C23
LCSG ▷ C257
UCSC1 ◁ C2×C4

162 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2056

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1659);