Finite Group Databasebeta

C2×#27132543 #37574939

order24448
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#27132543

Splittings

SylowC191 ⋊ C2×#386

Subgroups

subgroupG/H
centerC24C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
Fitting, prime radicalC23×D4×C191C2
socleC24×C191C23
cosocleC23×C191C24
hypercenterC23×D4D191
hypocenterC191C2×#386
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C24 ◁ C23×D4

1576 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, 6929);