Finite Group Databasebeta

C2×#19133197 #25064504

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133197

Splittings

SylowC43 ⋊ C2×#1528

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC22×#125×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C43C22⋊C4
cosocleC42×C43C24
hypercenterC22×#125D43
hypocenterC43C2×#1528
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#125

1050 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137475);