Finite Group Databasebeta

C2×#19133309 #25065112

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

Aliases

direct productC2×#19133309

Splittings

SylowC43 ⋊ C2×#1555

Subgroups

subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
Fitting, prime radicalC22×#127×C43C2
socleC23×C43C2×C22⋊C4
cosocleC42×C43C24
hypercenterC22×#127D43
hypocenterC43C2×#1555
LCSG ▷ C2×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C22×#127

1870 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1228 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 138083);