Finite Group Databasebeta

C2×#19133343 #25065571

order11008
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×#19133343

Splittings

SylowC43 ⋊ C2×#1564

Subgroups

subgroupG/H
centerC2×C42D172
commutatorC4×C43C23×C8
FrattiniC42C23×D43
FittingC22×C4×C8×C43C2
socleC23×C43C2×C4⋊C4
prime radicalC24×C43C4⋊C4
cosocleC42×C43C24
hypercenterC22×C4×C8D43
hypocenterC43C2×#1564
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C42 ◁ C22×C42 ◁ C22×C4×C8

830 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138542);