Finite Group Databasebeta

C2×#102×D191 #37581004

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C27

Aliases

direct productC2×#102×D191

Splittings

FittingC2×#102×C191 ⋊ C2
SylowC191 ⋊ C22×#102

Subgroups

subgroupG/H
centerC23D4×D191
commutatorC4×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#102×C191C2
socleC23×C191C2×D4
prime radicalC22×D4×D191C2
cosocleC2×C4×C191C24
hypercenterC2×#102D191
hypocenterC191C22×#102
LCSG ▷ C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#102

1072 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, 12994);