Finite Group Databasebeta

#407×D191 #37580953

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct product#407×D191

Splittings

Fitting#407×C191 ⋊ C2
SylowC191 ⋊ C2×#407

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D191
commutator, socleC22×C191C23×C4
Fitting#407×C191C2
prime radicalC24×D191C4
cosocleC2×C4×C191C24
hypercenter#407D191
hypocenterC191C2×#407
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ #407

1008 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, 12943);