Finite Group Databasebeta

C2×#27132791 #37581445

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27132791

Splittings

SylowC191 ⋊ C2×#446

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC2×C4C23×D191
FittingC2×#97×C191C2
socle, prime radicalC23×C191C22×C4
cosocleC2×C4×C191C24
hypercenterC2×#97D191
hypocenterC191C2×#446
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×#97

400 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

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, 13435);