Finite Group Databasebeta

C2×#19147458 #25977023

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

Aliases

direct productC2×#19147458

Splittings

FittingC2×C43×#554 ⋊ C2
SylowC43 ⋊ C2×#3380

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#554C2
socleC23×C43C22×D4
prime radicalC22×#10621882C22
hypercenterC2×#554D43
hypocenterC43C2×#3380
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

1918 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1049994);