Finite Group Databasebeta

C2×D2336 #22612229

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

Aliases

direct productC2×D2336

Splittings

FittingC2×C32×C73 ⋊ C2
SylowC73 ⋊ C2×D32

Subgroups

subgroupG/H
centerC22D1168
commutatorC16×C73C23
FrattiniC16C22×D73
FittingC2×C32×C73C2
socleC22×C73D16
hypercenterC2×C32D73
hypocenterC73C2×D32
LCSG ▷ C16×C73 ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2342 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#32973861, #32973863, #32973873, …
maximal normal subgroup of#32973861, #32973863, #32973873, …
maximal quotient ofC2×#22608110, C2×#22608131, C4×D2336, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 6808);