Finite Group Databasebeta

C2×C4×(C2×D191)⋊C4 #37574851

order24448
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D191)⋊C4

Splittings

FittingC22×C42×C191 ⋊ C2
SylowC191 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D191
commutatorC2×C191C22×C42
FrattiniC23C23×D191
FittingC22×C42×C191C2
socleC24×C191C23
prime radicalC24×D191C22
cosocleC23×C191C24
hypercenterC22×C42D191
hypocenterC191C2×C4×C22⋊C4
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

6160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6841);