Finite Group Databasebeta

C2×#19143872 #25963011

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

Aliases

direct productC2×#19143872

Splittings

SylowC43 ⋊ C2×#3009

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
Fitting, prime radicalC22×H(5,𝔽2)×C43C2
socleC23×C43C22×D4
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×#3009
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×#41 ◁ C22×H(5,𝔽2)

5062 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1492 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1035982);