Finite Group Databasebeta

#390×D241 #44509898

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

Aliases

direct product#390×D241

Splittings

Fitting#390×C241 ⋊ C2
SylowC241 ⋊ C2×#390

Subgroups

subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#390×C241C2
socle, cosocleC23×C241C24
prime radicalC22×D4×D241C2
hypercenter#390D241
hypocenterC241C2×#390
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #390

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7712

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, 6963);