Finite Group Databasebeta

C4×#20259287 #37574869

order24448
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC4×#20259287

Splittings

SylowC191 ⋊ C42×Q8

Subgroups

subgroupG/H
centerC22×C4C22×D191
commutatorC2×C191C22×C42
FrattiniC23C23×D191
FittingC4×C4⋊C4×C191C2
socle, prime radical, cosocleC23×C191C24
hypercenterC4×C4⋊C4D191
hypocenterC191C42×Q8
LCSG ▷ C2×C191 ▷ C191
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

684 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 24448

Conjugacy classes & character table

3880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24448, 6859);