Finite Group Databasebeta

C4×#14582881 #25094275

order11008
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C25×C4

Aliases

direct productC4×#14582881

Splittings

FittingC2×C4×M16×C43 ⋊ C2
SylowC43 ⋊ C4×#413

Subgroups

subgroupG/H
centerC42(C2×D43)⋊C4
commutatorC22×C43C22×C42
FrattiniC22×C4C23×D43
FittingC2×C4×M16×C43C2
socleC22×C43C22×C22⋊C4
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenterC2×C4×M16D43
hypocenterC43C4×#413
LCSG ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C42 ◁ C22×C42 ◁ C2×C4×M16

1570 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11008, 167246);