Finite Group Databasebeta

#389×D241 #44509892

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#389×D241

Splittings

Fitting#389×C241 ⋊ C2
SylowC241 ⋊ C2×#389

Subgroups

subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#389×C241C2
socle, cosocleC23×C241C24
prime radicalC23×D241C23
hypercenter#389D241
hypocenterC241C2×#389
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #389

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15424

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, 6957);