Finite Group Databasebeta

C2×#19137748 #25259190

order11008
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C27×C4

Aliases

direct productC2×#19137748

Splittings

FittingC2×C43×#388 ⋊ C2
SylowC43 ⋊ C2×#2377

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC22×#13063298C2
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2377
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

3302 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1252 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 332161);