Finite Group Databasebeta

C2×#17989516 #22626286

order9344
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#17989516

Splittings

SylowC73 ⋊ C2×#368

Subgroups

subgroupG/H
centerC22#14556660
commutatorC8×C73C22×C4
FrattiniC8C22×#64408
FittingC2×C16×C73C4
socleC22×C73#107
hypercenterC2×C16#64408
hypocenterC73C2×#368
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

620 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#34001078, #34001082, #34001087, …
maximal normal subgroup of#34001078, #34001082, #34001087, …
maximal quotient ofC2×#22624963, C2×#22624964, #34011756, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 20865);