Finite Group Databasebeta

C2×#17988569 #22618404

order9344
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC2×#17988569

Splittings

FittingC22×M16×C73 ⋊ C2
SylowC73 ⋊ C2×#413

Subgroups

subgroupG/H
centerC2×C4#11924005
commutatorC22×C73C23×C4
FrattiniC2×C4C23×D73
FittingC22×M16×C73C2
socleC22×C73C2×C22⋊C4
hypercenterC22×M16D73
hypocenterC73C2×#413
LCSG ▷ C22×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×M16

756 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1484 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#32991320, #32991323, #32991330, …
maximal normal subgroup of#32991320, #32991323, #32991330, …
maximal quotient ofC2×#22608243, C2×#22608247, #33051795, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(9344, 12983);