Finite Group Databasebeta

C2×#19135412 #25100242

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

Aliases

direct productC2×#19135412

Splittings

SylowC43 ⋊ C2×#1959

Subgroups

subgroupG/H
centerC24C2×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×#124×C43C2
socleC24×C43C2×D4
prime radicalC23×D4×C43C22
cosocleC22×C4×C43C24
hypercenterC22×#124D43
hypocenterC43C2×#1959
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C42 ◁ C22×#124

1814 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, 173213);