Finite Group Databasebeta

C4×#20259305 #37575042

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

Aliases

direct productC4×#20259305

Splittings

FittingC22×C42×C191 ⋊ C2
SylowC191 ⋊ C4×#123

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC22×C42×C191C2
socle, cosocleC23×C191C24
prime radicalC22×C22⋊D191C22
hypercenterC22×C42D191
hypocenterC191C4×#123
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C22×C42

688 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

6136 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7032);