Finite Group Databasebeta

#474×D191 #37582261

order24448
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C25

Aliases

direct product#474×D191

Splittings

Fitting#474×C191 ⋊ C2
SylowC191 ⋊ C2×#474

Subgroups

subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#474×C191C2
socleC22×C191C22×D4
prime radicalC2×D4×D191C22
hypercenter#474D191
hypocenterC191C2×#474
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #474

480 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

Conjugacy classes & character table

1843 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 14251);