Finite Group Databasebeta

#459×D191 #37581928

order24448
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct product#459×D191

Splittings

Fitting#459×C191 ⋊ C2
SylowC191 ⋊ C2×#459

Subgroups

subgroupG/H
centerC22C2×D4×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#459×C191C2
socleC22×C191C22×D4
hypercenter#459D191
hypocenterC191C2×#459
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C42 ◁ #459

648 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, 13918);