Finite Group Databasebeta

C2×#19136417 #25249750

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19136417

Splittings

FittingC2×C43×C22⋊C16 ⋊ C2
SylowC43 ⋊ C2×#2168

Subgroups

subgroupG/H
centerC22×C8C22×D43
commutatorC22×C43C23×C8
FrattiniC2×C8C23×D43
FittingC2×C43×C22⋊C16C2
socleC23×C43C22×C8
prime radicalC22×C22⋊D43C8
cosocleC2×C8×C43C24
hypercenterC2×C22⋊C16D43
hypocenterC43C2×#2168
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C8 ◁ C2×C22⋊C16

754 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1792 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 322721);