Finite Group Databasebeta

C2×#19137920 #25264148

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

Aliases

direct productC2×#19137920

Splittings

FittingC2×C43×#379 ⋊ C2
SylowC43 ⋊ C2×#2405

Subgroups

subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#379C2
socleC24×C43C24
prime radicalC24×C22⋊D43C2
hypercenterC2×#379D43
hypocenterC43C2×#2405
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#379

7822 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 337119);