Finite Group Databasebeta

#388×D241 #44509873

order30848
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25×C4

Aliases

direct product#388×D241

Splittings

Fitting#388×C241 ⋊ C2
SylowC241 ⋊ C2×#388

Subgroups

subgroupG/H
center, FrattiniC23C23×D241
commutatorC22×C241C23×C4
Fitting#388×C241C2
socle, cosocleC23×C241C24
prime radicalC24×D241C22
hypercenter#388D241
hypocenterC241C2×#388
LCSG ▷ C22×C241 ▷ C241
UCSC1 ◁ C23 ◁ #388

928 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, 6938);