Finite Group Databasebeta

C2×#27132538 #37574933

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

Aliases

direct productC2×#27132538

Splittings

SylowC191 ⋊ C2×#385

Subgroups

subgroupG/H
centerC24C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC22×C22⋊C4×C191C2
socleC24×C191C23
prime radicalC25×C191C22
cosocleC23×C191C24
hypercenterC22×C22⋊C4D191
hypocenterC191C2×#385
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C24 ◁ C22×C22⋊C4

1232 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3856 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6923);