Finite Group Databasebeta

C2×#19143058 #25960070

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143058

Splittings

FittingC2×C43×#519 ⋊ C2
SylowC43 ⋊ C2×#2884

Subgroups

subgroupG/H
centerC22C22×(C2×D43)⋊C4
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#519C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#13063373C2
cosocleC23×C43C25
hypercenterC2×#519D43
hypocenterC43C2×#2884
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×Q8 ◁ C2×#519

4818 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1510 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1033041);