Finite Group Databasebeta

C2×#19133099 #25063737

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

Aliases

direct productC2×#19133099

Splittings

SylowC43 ⋊ C2×#1504

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
Fitting, prime radicalC2×C43×#525C2
socleC23×C43C2×C22⋊C4
cosocleC22×C4×C43C24
hypercenterC2×#525D43
hypocenterC43C2×#1504
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#525

1834 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 136708);