Finite Group Databasebeta

#117×Dic191 #37574863

order24448
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct product#117×Dic191

Splittings

SylowC191 ⋊ C4×#117

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC2×C191C22×C42
FrattiniC23C23×D191
FittingC2×#117×C191C2
socle, cosocleC23×C191C24
prime radicalC24×C191C23
hypercenterC2×#117D191
hypocenterC191C4×#117
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×#117

752 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6853);