Finite Group Databasebeta

#344×D191 #37572260

order24448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct product#344×D191

Splittings

Fitting#344×C191 ⋊ C2
SylowC191 ⋊ C2×#344

Subgroups

subgroupG/H
centerC4C22⋊C4×D191
commutatorC22×C191C2×C42
FrattiniC22×C4C22×D191
Fitting#344×C191C2
socleC2×C191C2×#95
prime radicalC23×D191C2×C4
cosocleC22×C4×C191C23
hypercenter#344D191
hypocenterC191C2×#344
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C4 ◁ C22×C4 ◁ #344

388 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3056

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, 4250);