Finite Group Databasebeta

C2×#17989696 #22627163

order9344
automorphism?
homologyAbelianization (H1) = C22×C16 · Schur multiplier (H2) = C22

Aliases

direct productC2×#17989696

Splittings

SylowC73 ⋊ C2×M64

Subgroups

subgroupG/H
centerC2×C4C2×#10596842
commutatorC2×C73C22×C16
FrattiniC4C22×#10596842
FittingC2×C8×C73C8
socleC22×C73C2×C16
hypercenterC2×C8#10596842
hypocenterC73C2×M64
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C8

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

224 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34033132, #34033141, C4×#17989696, …
maximal normal subgroup of#34033132, #34033141, C4×#17989696, …
maximal quotient ofC2×#22627017, C4×#17989696, C2×#22627024, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 21742);