Finite Group Databasebeta

C2×#19143992 #25963325

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

Aliases

direct productC2×#19143992

Splittings

FittingC22×H(5,𝔽2)×C43 ⋊ C2
SylowC43 ⋊ C2×#3026

Subgroups

subgroupG/H
centerC22C2×#13063294
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×H(5,𝔽2)×C43C2
socleC22×C43C2×#120
hypercenterC22×H(5,𝔽2)D43
hypocenterC43C2×#3026
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C25 ◁ C22×H(5,𝔽2)

5318 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1486 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 1036296);