Finite Group Databasebeta

C2×#103×D191 #37581008

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#103×D191

Splittings

FittingC2×#103×C191 ⋊ C2
SylowC191 ⋊ C22×#103

Subgroups

subgroupG/H
centerC23D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#103×C191C2
socleC23×C191C2×D4
prime radicalC23×D191D4
cosocleC2×C4×C191C24
hypercenterC2×#103D191
hypocenterC191C22×#103
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

816 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, 12998);