Finite Group Databasebeta

D4×#14523346 #30657763

order16448
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productD4×#14523346

Splittings

SylowC257 ⋊ C8×D4

Subgroups

subgroupG/H
center, FrattiniC22C22×#11759967
commutatorC2×C257C22×C8
Fitting, prime radicalC2×D4×C257C4
socleC22×C257C22×C4
cosocleC2×Dic257C23
hypercenterC2×D4#11759967
hypocenterC257C8×D4
LCSG ▷ C2×C257 ▷ C257
UCSC1 ◁ C22 ◁ C2×D4

134 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8224

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16448, 1575);