Finite Group Databasebeta

C2×#19136952 #25254807

order11008
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C28×C4

Aliases

direct productC2×#19136952

Splittings

SylowC43 ⋊ C2×#2274

Subgroups

subgroupG/H
centerC24C23×D43
commutatorC2×C43C23×C42
FrattiniC23C24×D43
FittingC23×C4⋊C4×C43C2
socleC24×C43C24
prime radicalC25×C43C23
cosocleC23×C43C25
hypercenterC23×C4⋊C4D43
hypocenterC43C2×#2274
LCSG ▷ C2×C43 ▷ C43
UCSC1 ◁ C24 ◁ C23×C4⋊C4

4110 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1816 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 327778);