Finite Group Databasebeta

C2×#17988425 #22612232

order9344
automorphism?
homologyAbelianization (H1) = C23 · Schur multiplier (H2) = C22

Aliases

direct productC2×#17988425

Splittings

SylowC73 ⋊ C2×SD64

Subgroups

subgroupG/H
centerC22#14556532
commutatorC16×C73C23
FrattiniC16C22×D73
FittingC2×D16×C73C2
socleC22×C73D16
hypercenterC2×D16D73
hypocenterC73C2×SD64
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×D16

112 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

830 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×#17988425, #33006566, #33006572, …
maximal normal subgroup ofC4×#17988425, #33006566, #33006572, …
maximal quotient ofC2×#22608109, C2×#22608111, C2×#22608132, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 6811);