Finite Group Databasebeta

C2×#17989470 #22625642

order9344
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C24

Aliases

direct productC2×#17989470

Splittings

FittingC2×M16×C73 ⋊ C4
SylowC73 ⋊ C2×#344

Subgroups

subgroupG/H
centerC22(C2×#64408)⋊C4
commutatorC22×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC2×M16×C73C4
socleC22×C73#95
hypercenterC2×M16#64408
hypocenterC73C2×#344
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#17989470, #34008314, #34008369, …
maximal normal subgroup ofC4×#17989470, #34008314, #34008369, …
maximal quotient ofC2×#22624770, #34002250, #34002253, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 20221);