Finite Group Databasebeta

#376×D191 #37574845

order24448
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C42

Aliases

direct product#376×D191

Splittings

Fitting#376×C191 ⋊ C2
SylowC191 ⋊ C2×#376

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC2×C191C22×C42
FrattiniC23C23×D191
Fitting#376×C191C2
socle, cosocleC23×C191C24
prime radicalC23×D191C23
hypercenter#376D191
hypocenterC191C2×#376
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ #376

840 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, 6835);