Finite Group Databasebeta

C2×#19145165 #25966323

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19145165

Splittings

FittingC22×C4×C8×C43 ⋊ C2
SylowC43 ⋊ C2×#3168

Subgroups

subgroupG/H
centerC22×C4C2×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×C4×C8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583135C2
hypercenterC22×C4×C8D43
hypocenterC43C2×#3168
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×C4×C8

2070 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2776 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1039294);