Finite Group Databasebeta

#322×D191 #37570794

order24448
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C22×C4

Aliases

direct product#322×D191

Splittings

Fitting#322×C191 ⋊ C2
SylowC191 ⋊ C2×#322

Subgroups

subgroupG/H
center, FrattiniC42C22×D191
commutatorC2×C191C2×C4×C8
Fitting#322×C191C2
socleC22×C191C2×C42
prime radicalC22×D191C42
cosocleC42×C191C23
hypercenter#322D191
hypocenterC191C2×#322
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C42 ◁ #322

248 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, 2784);