Finite Group Databasebeta

C2×#17989459 #22625609

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

Aliases

direct productC2×#17989459

Splittings

FittingC2×M16×C73 ⋊ C4
SylowC73 ⋊ C2×#339

Subgroups

subgroupG/H
centerC2×C4C22⋊#64408
commutatorC4×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC2×M16×C73C4
socleC22×C73#95
hypercenterC2×M16#64408
hypocenterC73C2×#339
LCSG ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

488 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

416 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#339×#64408, C4×#17989459, #34008270, …
maximal normal subgroup of#339×#64408, C4×#17989459, #34008270, …
maximal quotient ofC2×#22624758, #34002030, #34002037, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 20188);