Finite Group Databasebeta

C2×#19147266 #25976193

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C28

Aliases

direct productC2×#19147266

Splittings

FittingC2×Q82×C43 ⋊ C2
SylowC43 ⋊ C2×#3362

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×Q82×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583571C2
hypercenterC2×Q82D43
hypocenterC43C2×#3362
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×Q82

2174 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1049164);