Finite Group Databasebeta

C2×#19132950 #25062550

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19132950

Splittings

SylowC43 ⋊ C2×#1470

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#431C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22×C4
cosocleC22×C4×C43C24
hypercenterC2×#431D43
hypocenterC43C2×#1470
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#431

1002 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135521);