Finite Group Databasebeta

#472×D191 #37582223

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

Aliases

direct product#472×D191

Splittings

Fitting#472×C191 ⋊ C2
SylowC191 ⋊ C2×#472

Subgroups

subgroupG/H
centerC2#121×D191
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#472×C191C2
socleC2×C191C2×#121
hypercenter#472D191
hypocenterC191C2×#472
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C2 ◁ C2×C4 ◁ #472

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3056

Conjugacy classes & character table

1552 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 14213);