Finite Group Databasebeta

C2×#27132592 #37575748

order24448
automorphism?
homologyAbelianization (H1) = C24 · Schur multiplier (H2) = C26

Aliases

direct productC2×#27132592

Splittings

FittingC2×#95×C191 ⋊ C2
SylowC191 ⋊ C2×#397

Subgroups

subgroupG/H
centerC24C22×D191
commutator, cosocleC23×C191C24
FrattiniC23C23×D191
FittingC2×#95×C191C2
socleC24×C191C23
prime radicalC24×D191C22
hypercenterC2×#95D191
hypocenterC191C2×#397
LCSG ▷ C23×C191 ▷ C191
UCSC1 ◁ C24 ◁ C2×#95

820 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12224

Conjugacy classes & character table

3844 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 7738);