Finite Group Databasebeta

#344×D241 #44507185

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

Aliases

direct product#344×D241

Splittings

Fitting#344×C241 ⋊ C2
SylowC241 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D241
commutatorC22×C241C2×C42
FrattiniC22×C4C22×D241
Fitting#344×C241C2
socleC2×C241C2×#95
prime radicalC23×D241C2×C4
cosocleC22×C4×C241C23
hypercenter#344D241
hypocenterC241C2×#344
LCSG ▷ C22×C241 ▷ C2×C241 ▷ C241
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3856

Conjugacy classes & character table

2684 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30848, 4250);