Finite Group Databasebeta

#339×D241 #44507149

order30848
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#339×D241

Splittings

Fitting#339×C241 ⋊ C2
SylowC241 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4D4×D241
commutatorC4×C241C2×C42
FrattiniC22×C4C22×D241
Fitting#339×C241C2
socleC22×C241C2×C22⋊C4
prime radicalC23×D241D4
cosocleC22×C4×C241C23
hypercenter#339D241
hypocenterC241C2×#339
LCSG ▷ C4×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3856

Conjugacy classes & character table

3416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 4214);