Finite Group Databasebeta

#123×Dic191 #37575043

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

Aliases

direct product#123×Dic191

Splittings

SylowC191 ⋊ C4×#123

Subgroups

subgroupG/H
center, FrattiniC23C23×D191
commutatorC22×C191C23×C4
FittingC2×#123×C191C2
socle, cosocleC23×C191C24
prime radicalC22×D4×C191C22
hypercenterC2×#123D191
hypocenterC191C4×#123
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C23 ◁ C2×#123

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

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, 7033);