Finite Group Databasebeta

C4×#20259312 #37575076

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

Aliases

direct productC4×#20259312

Splittings

SylowC191 ⋊ C4×#125

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC22×C191C23×C4
FrattiniC23C23×D191
FittingC4×C4⋊C4×C191C2
socle, prime radical, cosocleC23×C191C24
hypercenterC4×C4⋊C4D191
hypocenterC191C4×#125
LCSG ▷ C22×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

484 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, 7066);