Finite Group Databasebeta

C2×#17989469 #22625640

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

Aliases

direct productC2×#17989469

Splittings

FittingC22×C8×C73 ⋊ C4
SylowC73 ⋊ C2×#344

Subgroups

subgroupG/H
centerC2×C4C22⋊#64408
commutatorC22×C73C2×C42
FrattiniC2×C4C22×#64408
FittingC22×C8×C73C4
socleC22×C73#95
hypercenterC22×C8#64408
hypocenterC73C2×#344
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8

388 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

620 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#17989469, #34008307, #34008312, …
maximal normal subgroup ofC4×#17989469, #34008307, #34008312, …
maximal quotient ofC2×#22624771, #34002251, #34002255, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 20219);