Finite Group Databasebeta

#339×D239 #44484252

order30592
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D239

Splittings

Fitting#339×C239 ⋊ C2
SylowC239 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D239
commutatorC4×C239C2×C42
FrattiniC22×C4C22×D239
Fitting#339×C239C2
socleC22×C239C2×C22⋊C4
prime radicalC23×D239D4
cosocleC22×C4×C239C23
hypercenter#339D239
hypocenterC239C2×#339
LCSG ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3824

Conjugacy classes & character table

3388 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30592, 4214);