Finite Group Databasebeta

C2×#19132589 #25006755

order11008
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C23

Aliases

direct productC2×#19132589

Splittings

SylowC43 ⋊ C2×#1342

Subgroups

subgroupG/H
centerC22#14582633
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC2×C43×#470C2
socleC22×C43#327
prime radicalC24×C43SD16
cosocleC2×M16×C43C23
hypercenterC2×#470D43
hypocenterC43C2×#1342
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×M16 ◁ C2×#470

428 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

712 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 79726);