Finite Group Databasebeta

C2×#19144225 #25963755

order11008
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct productC2×#19144225

Splittings

FittingC23×M16×C43 ⋊ C2
SylowC43 ⋊ C2×#3056

Subgroups

subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC23×M16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583410C2
hypercenterC23×M16D43
hypocenterC43C2×#3056
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C23×M16

2898 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, 1036726);