Finite Group Databasebeta

M16×#10621877 #25062307

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C4

Aliases

direct productM16×#10621877

Splittings

SylowC43 ⋊ M162

Subgroups

subgroupG/H
center, FrattiniC42C23×D43
commutator, socleC22×C43C22×C42
FittingC2×C4×M16×C43C2
prime radicalC24×C43C42
cosocleC42×C43C24
hypercenterC2×C4×M16D43
hypocenterC43M162
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C42 ◁ C2×C4×M16

900 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1780 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 135278);