Finite Group Databasebeta

C2×C4×(C2×#6157)⋊C4 #28312677

order13568
automorphism?
homologyAbelianization (H1) = C2×C43 · Schur multiplier (H2) = C26×C42

Aliases

direct productC2×C4×(C2×#6157)⋊C4

Splittings

FittingC22×C42×C53 ⋊ C4
SylowC53 ⋊ C2×C4×#95

Subgroups

subgroupG/H
centerC23×C4C2×#6157
commutatorC2×C53C2×C43
FrattiniC23C23×#6157
FittingC22×C42×C53C4
socleC24×C53C22×C4
prime radicalC24×D53C23
cosocleC23×D53C24
hypercenterC22×C42#6157
hypocenterC53C2×C4×#95
LCSG ▷ C2×C53 ▷ C53
UCSC1 ◁ C23×C4 ◁ C22×C42

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3392

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(13568, 1098153);