Finite Group Databasebeta

C2×#19133181 #25064479

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C25

Aliases

direct productC2×#19133181

Splittings

FittingC22×#97×C43 ⋊ C2
SylowC43 ⋊ C2×#1524

Subgroups

subgroupG/H
centerC22×C4(C2×D43)⋊C4
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingC22×#97×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#13063299C4
cosocleC42×C43C24
hypercenterC22×#97D43
hypocenterC43C2×#1524
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C22×C42 ◁ C22×#97

1166 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1756 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 137450);