Finite Group Databasebeta

#389×D191 #37574967

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#389×D191

Splittings

Fitting#389×C191 ⋊ C2
SylowC191 ⋊ C2×#389

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
Fitting#389×C191C2
socle, cosocleC23×C191C24
prime radicalC23×D191C23
hypercenter#389D191
hypocenterC191C2×#389
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ #389

800 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6957);