Finite Group Databasebeta

M16×#10621883 #25068033

order11008
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C24

Aliases

direct productM16×#10621883

Splittings

SylowC43 ⋊ M16×SD16

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D43
commutatorC2×C4×C43C23×C4
FrattiniC42C23×D43
FittingD4×M16×C43C2
socleC22×C43C2×C4×D4
prime radicalC22×D4×C43C2×C4
cosocleC42×C43C24
hypercenterD4×M16D43
hypocenterC43M16×SD16
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ D4×M16

716 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1120 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 141004);