Finite Group Databasebeta

C2×#19134509 #25095719

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19134509

Splittings

FittingC2×C43×#379 ⋊ C2
SylowC43 ⋊ C2×#1781

Subgroups

subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#379C2
socleC23×C43C2×C22⋊C4
prime radicalC24×C22⋊D43C2
cosocleC24×C43C24
hypercenterC2×#379D43
hypocenterC43C2×#1781
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C26 ◁ C2×#379

6254 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, 168690);