Finite Group Databasebeta

C2×#17988417 #22611723

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

Aliases

direct productC2×#17988417

Splittings

SylowC73 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D584
commutatorC8×C73C22×C4
FrattiniC2×C8C22×D73
FittingC22×C16×C73C2
socleC22×C73#107
hypercenterC22×C16D73
hypocenterC73C2×#368
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2348 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#32973686, #32973687, #32973688, …
maximal normal subgroup of#32973686, #32973687, #32973688, …
maximal quotient ofC2×#22608003, C2×#22608005, #32997569, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 6302);