Finite Group Databasebeta

C2×#19134866 #25097537

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#19134866

Splittings

SylowC43 ⋊ C2×#1865

Subgroups

subgroupG/H
centerC24C2×D172
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#336C2
socle, prime radicalC24×C43C2×D4
cosocleC22×C4×C43C24
hypercenterC2×#336D43
hypocenterC43C2×#1865
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C2×#336

1542 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, 170508);