Finite Group Databasebeta

C2×#19137918 #25264150

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19137918

Splittings

SylowC43 ⋊ C2×#2405

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
Fitting, prime radicalC24×D4×C43C2
socleC24×C43C24
hypercenterC24×D4D43
hypocenterC43C2×#2405
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C24×D4

7822 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, 337121);