Finite Group Databasebeta

C2×#17989681 #22627086

order9344
automorphism?
homologyAbelianization (H1) = C2×C4×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×#17989681

Splittings

SylowC73 ⋊ C2×#346

Subgroups

subgroupG/H
centerC23C2×#10596842
commutatorC2×C73C2×C4×C8
FrattiniC22C22×#10596842
FittingC22×C4×C73C8
socleC23×C73C2×C8
hypercenterC22×C4#10596842
hypocenterC73C2×#346
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34032864, #34032909, #34032920, …
maximal normal subgroup of#34032864, #34032909, #34032920, …
maximal quotient ofC2×#22626947, C2×#22626949, #34033502, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 21665);