Finite Group Databasebeta

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C2×M16×Dic73 #22618338

order9344
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C24×C4

Aliases

direct productC2×M16×Dic73

Splittings

SylowC73 ⋊ C2×C4×M16

Subgroups

subgroupG/H
centerC22×C4C22×D73
commutatorC2×C73C22×C42
FrattiniC2×C4C23×D73
FittingC22×M16×C73C2
socleC23×C73C22×C4
hypercenterC22×M16D73
hypocenterC73C2×C4×M16
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C22×M16

656 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1520 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofH(3,ℤ/4)×Dic73, #338×Dic73, #339×Dic73, …
maximal normal subgroup ofH(3,ℤ/4)×Dic73, #338×Dic73, #339×Dic73, …
maximal quotient ofC2×M16×#10596831, C2×#22608212, C2×#22608218, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 12917);