Finite Group Databasebeta

C4×#20259309 #37575062

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

Aliases

direct productC4×#20259309

Splittings

SylowC191 ⋊ C4×#124

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC2×C4×D4×C191C2
socle, cosocleC23×C191C24
prime radicalC22×D4×C191C22
hypercenterC2×C4×D4D191
hypocenterC191C4×#124
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C2×C4×D4

652 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, 7052);