Finite Group Databasebeta

C2×#17989464 #22625626

order9344
automorphism?
homologyAbelianization (H1) = C2×C42 · Schur multiplier (H2) = C25

Aliases

direct productC2×#17989464

Splittings

FittingC2×C22⋊C4×C73 ⋊ C4
SylowC73 ⋊ C2×#342

Subgroups

subgroupG/H
centerC22(C2×#64408)⋊C4
commutatorC22×C73C2×C42
FrattiniC23C22×#64408
FittingC2×C22⋊C4×C73C4
socleC22×C73#95
hypercenterC2×C22⋊C4#64408
hypocenterC73C2×#342
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C24 ◁ C2×C22⋊C4

680 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

404 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#342×#64408, C4×#17989464, #34008353, …
maximal normal subgroup of#342×#64408, C4×#17989464, #34008353, …
maximal quotient ofC2×#22624768, #34002211, #34002217, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 20205);