Finite Group Databasebeta

#137×Dic191 #37581341

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct product#137×Dic191

Splittings

SylowC191 ⋊ C4×#137

Subgroups

subgroupG/H
centerC22C2×D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#137×C191C2
socleC22×C191C22×D4
prime radicalC2×#41×C191C22
cosocleC2×C4×C191C24
hypercenterC2×#137D191
hypocenterC191C4×#137
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

484 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

2134 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13331);