Finite Group Databasebeta

C2×#31823293 #49097095

order35968
automorphism?
homologyAbelianization (H1) = C22×C4 · Schur multiplier (H2) = C22

Aliases

direct productC2×#31823293

Splittings

SylowC281 ⋊ C2×#368

Subgroups

subgroupG/H
centerC2×C4D2248
commutatorC8×C281C22×C4
FrattiniC2×C8C22×D281
FittingC22×C16×C281C2
socleC22×C281#107
prime radicalC23×C281Q16
cosocleC2×C8×C281C23
hypercenterC22×C16D281
hypocenterC281C2×#368
LCSG ▷ C8×C281 ▷ C4×C281 ▷ C2×C281 ▷ C281
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C22×C8 ◁ C22×C16

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 17984

Conjugacy classes & character table

9004 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(35968, 6302);