Finite Group Databasebeta

C4×#14583044 #25102212

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#14583044

Splittings

FittingC2×C4×#41×C43 ⋊ C2
SylowC43 ⋊ C4×#449

Subgroups

subgroupG/H
centerC22×C4C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C4×#41×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583044C2
cosocleC22×C4×C43C24
hypercenterC2×C4×#41D43
hypocenterC43C4×#449
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C2×C4×#41

1564 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 175183);