Finite Group Databasebeta

C2×#19135054 #25098385

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×#19135054

Splittings

SylowC43 ⋊ C2×#1899

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC22×#123×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×D4×C43C22
cosocleC24×C43C24
hypercenterC22×#123D43
hypocenterC43C2×#1899
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×#123

2066 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, 171356);