Finite Group Databasebeta

C2×#27132431 #37572255

order24448
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#27132431

Splittings

SylowC191 ⋊ C2×#343

Subgroups

subgroupG/H
centerC23(C2×D191)⋊C4
commutatorC22×C191C2×C42
FrattiniC22×C4C22×D191
FittingC22×M16×C191C2
socleC23×C191C22⋊C4
prime radicalC24×C191C2×C4
cosocleC22×C4×C191C23
hypercenterC22×M16D191
hypocenterC191C2×#343
LCSG ▷ C22×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×M16

432 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, 4245);