Finite Group Databasebeta

C2×C4×(C2×D283)⋊C4 #49123592

order36224
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C26×C4

Aliases

direct productC2×C4×(C2×D283)⋊C4

Splittings

FittingC22×C42×C283 ⋊ C2
SylowC283 ⋊ C2×C4×C22⋊C4

Subgroups

subgroupG/H
centerC23×C4C2×D283
commutatorC2×C283C22×C42
FrattiniC23C23×D283
FittingC22×C42×C283C2
socleC24×C283C23
prime radicalC24×D283C22
cosocleC23×C283C24
hypercenterC22×C42D283
hypocenterC283C2×C4×C22⋊C4
LCSG ▷ C2×C283 ▷ C283
UCSC1 ◁ C23×C4 ◁ C22×C42

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 18112

Conjugacy classes & character table

9104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36224, 6841);