Finite Group Databasebeta

← Prev (#20283121) Next (#20283123) →

C2×M16×Dic53 #20283122

order6784
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic53

Splittings

SylowC53 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D53
commutatorC2×C53C22×C42
FrattiniC2×C4C23×D53
FittingC22×M16×C53C2
socleC23×C53C22×C4
hypercenterC22×M16D53
hypocenterC53C2×C4×M16
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

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

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic53, #338×Dic53, #339×Dic53, …
maximal normal subgroup ofH(3,ℤ/4)×Dic53, #338×Dic53, #339×Dic53, …
maximal quotient ofC2×M16×#88322, C2×#20272996, C2×#20273002, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6784, 12917);