Finite Group Databasebeta

#443×D191 #37581406

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

Aliases

direct product#443×D191

Splittings

Fitting#443×C191 ⋊ C2
SylowC191 ⋊ C2×#443

Subgroups

subgroupG/H
centerC8D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
Fitting#443×C191C2
socleC2×C191C2×C4×D4
prime radical#135×D191C2
cosocleC2×C4×C191C24
hypercenter#443D191
hypocenterC191C2×#443
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C8 ◁ C2×C8 ◁ #443

472 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3056

Conjugacy classes & character table

2716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13396);