Finite Group Databasebeta

C2×#19143829 #25962952

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C210

Aliases

direct productC2×#19143829

Splittings

FittingC24×Q8×C43 ⋊ C2
SylowC43 ⋊ C2×#3004

Subgroups

subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC24×Q8×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenterC24×Q8D43
hypocenterC43C2×#3004
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C24×Q8

4970 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1744 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1035923);