Finite Group Databasebeta

#432×D191 #37581137

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

Aliases

direct product#432×D191

Splittings

Fitting#432×C191 ⋊ C2
SylowC191 ⋊ C2×#432

Subgroups

subgroupG/H
center, FrattiniC2×C4C23×D191
commutator, socleC22×C191C23×C4
Fitting#432×C191C2
prime radicalC23×D191C2×C4
cosocleC2×C4×C191C24
hypercenter#432D191
hypocenterC191C2×#432
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C2×C4 ◁ #432

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

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, 13127);