Finite Group Databasebeta

#431×D191 #37581132

order24448
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct product#431×D191

Splittings

Fitting#431×C191 ⋊ C2
SylowC191 ⋊ C2×#431

Subgroups

subgroupG/H
centerC42C22×D191
commutatorC2×C191C23×C8
FrattiniC2×C4C23×D191
Fitting#431×C191C2
socleC22×C191C23×C4
prime radicalC23×D191C2×C4
cosocleC2×C4×C191C24
hypercenter#431D191
hypocenterC191C2×#431
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C42 ◁ #431

528 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6112

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 13122);