Finite Group Databasebeta

C2×#19132603 #25006815

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C24

Aliases

direct productC2×#19132603

Splittings

FittingC2×C43×#340 ⋊ C2
SylowC43 ⋊ C2×#1347

Subgroups

subgroupG/H
centerC23#13063245
commutatorC2×C8×C43C22×C4
FrattiniC22×C8C22×D43
FittingC2×C43×#340C2
socleC23×C43#102
prime radicalC2×#14583135C2
cosocleC22×C8×C43C23
hypercenterC2×#340D43
hypocenterC43C2×#1347
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ C2×#340

558 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1234 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 79786);