Finite Group Databasebeta

C2×C22⋊C8×D283 #49129691

order36224
automorphism?
homologyAbelianization (H1) = C23×C8 · Schur multiplier (H2) = C27

Aliases

direct productC2×C22⋊C8×D283

Splittings

FittingC2×C22⋊C8×C283 ⋊ C2
SylowC283 ⋊ C22×C22⋊C8

Subgroups

subgroupG/H
centerC22×C4C22×D283
commutatorC2×C283C23×C8
FrattiniC2×C4C23×D283
FittingC2×C22⋊C8×C283C2
socleC23×C283C22×C4
prime radicalC24×D283C4
cosocleC2×C4×C283C24
hypercenterC2×C22⋊C8D283
hypocenterC283C22×C22⋊C8
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

1072 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9056

Conjugacy classes & character table

5720 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 12940);